First of all, the debate resolution, which is, once again, "1 and .999 repeating are the same quantity. Exactly equal." says absolutely nothing about mathematics or rules or axioms or authority or popularity. So technically, and I do like to get technical, "1" is only one character and ".999 repeating" is fourteen characters including the space, therefore they are not the same quantity of characters and the resolution is technically defeated.
Second of all, for Mhykiel, if you wanted to use google info, you should have made those references explicit within the actual debate. Appealing to a third party will get you nowhere at this point, either make your own case with logic or I remain unconvinced.
And to drafterman, when you say, "All numbers are "finite" because "infinity" isn't a number. The second number would require an [][]infinite number[][] of digits to represent in written form, but we needn't worry about that because we have the [][]appropriate symbols[][] (r) to account for those infinite digits."
How is that substantively different from the idea that "There is an infinitesimal difference of 0.0000(r)1, which is a non-zero value."?
If we have, as you say, "...the appropriate symbols (r) to account for those infinite digits." it does not follow that the symbol referenced "(r)" could not have a number after it or that we couldn't use some other form of notation to identify the infinitesimal.
I'm also not sure how you can say, "infinite number" right after you say, "infinity is not a number".
"Them's the rules" is missing from the debate resolution.
I would cordially like to invite each of you to present your preferred definitions of "infinitesimal" for further examination.
In order to resolve the disagreement in viewpoints, each side builds a case with logical support.
You begin this process by stating explicit definitions and then addressing any conflicts between the PRO and CON definitions individually as they are identified.
This process is called "identifying common ground".
Once common ground is identified, then a logical case is built by both sides (upon the agreed negotiated definitions) and errors are identified by each opponent.
The point of Civil Debate is to actually resolve conflict and not simply to bully your opponent into submission.
If the definitions are not explicitly agreed upon, then both sides are able to build cases that may use similar words but actually have nothing to do with each other which results in two people talking past each other without realizing they are debating two completely different topics.
The problem identified by PRO (highlighted by the resolution itself) is a limitation (flaw) of the decimal system, not a limitation of common fractions.
My stated supporting argument directly addresses the debate resolution.
RationalMadman seemed to think that, "Your resolution is impossible because: EITHER We round and get 1 and/or 3. OR We don't round and admit that '7' which is missing in that 0.9recurring * 3 so it can never truly be 3 and thus 3/3 can't be 0.9recurring. Checkmate." closed their case.
However, RationalMadman's argument does not directly address the debate resolution.
The following steel man actually does directly address the debate resolution.
Therefore, "1 and .999 repeating are the same quantity. Exactly equal." is false.
I have no idea why you found my previous comments "annoying and non-productive" since both of these are negative characterizations (ad hominem) and not strictly legitimate objections to my logic.
I really and truly would like to clear up any questions or misunderstandings you or anyone else might have.
Destroying your opponents examples (supporting arguments) alone does not make your case.
That would be like merely blocking your opponent from making a goal.
You actually have to make a goal yourself in order to get a point.
0.8888888888(r) + 0.1111111111111(r) = 0.99999999999999(r) =/= 1.0000000000(r)
Therefore, "1 and .999 repeating are the same quantity. Exactly equal." is false.
If you disagree, please present your argument that disproves my argument or in some other way affirms the debate resolution of "1 and .999 repeating are the same quantity. Exactly equal."
Do you for instance, honestly believe that 0.8888888888888(r) + 0.1111111111111(r) = 1.000000000000(r) ?????????????????(r)
I really and truly would like to clear up any questions or misunderstandings you might have, but at this point you sound like a broken record.
When you say, (IFF) "He's not saying that there's a 1 at the "end". He's saying that it's a mistake to think that there's a 1 at the end." (THEN) how do the "9's" ever change? Why don't they stay exactly 0.9999999999999999(r) if there is no way to convert them into anything else?
When I first read debate, I thought of the classic A =/= A argument. However this seems to be a case of A = A.00000000000(r)0000000000001 which is quantifiably false.
Therefore, by PRO's own logic in quote number one, since an infinite set of zeros with a 1 at the end is not exactly and precisely the same as zero, they magically round up to the target value of "1". Because if 1.0 and 0.999(r) were eXactly the same, then the result would obviously be actual zero.
Therefore, "1 and .999 repeating are the same quantity. Exactly equal." is false.
Not to mention 0.8888888888(r) + 0.1111111111111(r) =/= 1.0000000000(r)
And even if I quote from your previous comment, "Pro's case was that 0.999r must be 1 because 1/3 = 0.333r and 2/3 = .666r and 1/3 + 2/3 = 3/3 = 1. It's a pretty weak case but it doesn't have anything to do with rounding." this is also provably false because 0.333(r) and 0.666(r) approach 1/3 and 2/3 respectively but they require rounding.
Since you can never type out infinite anything, anything ending in an infinite sequence must (EITHER) be typed out explicitly (OR) rounded (like pi).
And I quote from round 2, (1)"We can confirm this because of the additive identity. identity property of addition, which simply states that when you add zero to any number, it equals the number itself. So if the difference between 2 numbers is not zero. They are not equal."
And I quote again from round 2, (2)"If we take 1 and subtract .999 repeating we are quick to say the answer is an infinite set of zeros then a 1. ie .00000..infinity..somehow ends in a 1. But those zeroes go on for infinity. That singular "1" never appears. Making the answer to what is "1" minus ".999 repeating" equal to an infinite set of zeroes."
Therefore, by PRO's own logic in quote number one, since an infinite set of zeros with a 1 at the end is not exactly and precisely the same as zero, they magically round up to the target value of "1". Because if 1.0 and 0.999(r) were eXactly the same, then the result would obviously be actual zero.
This is literally rounding 0.0000(r)0001 to 0.0000(r). PRO stakes their case on rounding. This defeats the debate resolution.
HOwever, I did not give the "arguments" points to CON because CON failed to clearly identify this error in logic.
You also make a good parallel case, and I applaud your excellent steel man, but I am not fabricating a new argument, I have based my critique on CON's actual statements.
When you said, and I quote from your RFD, "Pro correctly pointed out that no rounding was being supposed.", this statement is provably false.
Civil Debate - Rule One: You cannot redefine truth.
Every definition of truth requires facts.
Facts are indisputable.
Just like a court of law, both the prosecution and defense must agree on the facts.
If you and your opponent disagree about a fact, you must immediately stop the debate and negotiate the point of disputed fact.
Civil Debate - Rule Two: Do not disqualify your opponent.
Just like a boxing champion, you are only as good as your opponent.
Ridicule is below the belt.
Use logic.
Your identity cannot qualify or disqualify sound logic.
Civil Debate - Rule Three: Only your opponent can award points.
When your opponent makes a valid objection, you have the option to award them a point.
Valid objections strengthen your argument.
Help your opponent strengthen their position by presenting a steel man.
The best debates are the ones that force you to learn something new.
When Death23 makes the bare assertion, "Pro correctly pointed out that no rounding was being supposed." this is provably false.
What PRO actually argues is that the difference between 1.00000(r) and 0.999999(r) is 0.00000(any number)00000010000(r) which is according to PRO "impossible" and therefore virtually equivalent to zero. However, by notating 0.00000(any number)00000010000(r) it would seem to be no more "impossible" than 0.999999(r) or any other "infinite" sequence (like pi).
0.8888888888(r) + 0.1111111111(r) =/= 1.00000(r)
I would call this a tie on arguments, because CON fails to make a clear case, but I'd consider making a case to award points to PRO for conduct.
Round one PRO - "Hello, I appreciate my challenger taking me up this debate. Good luck to you Sir/Ma'am" which is polite.
Round one CON - "...Pro is tricking you..." which is a negative characterization ad hominem strongly suggesting that PRO is intentionally deceptive.
Round one CON - "'I am smart and good at math'" which is not only a bald assertion but also an indirect ad hominem directed at PRO.
Round two PRO - "Thank you Mad for the quick reply." which is polite.
Round two CON - "You're completely deceiving the reader..." which is a negative characterization ad hominem strongly suggesting that PRO is intentionally deceptive.
Round two CON - "Checkmate." which is a rush-to-declare-victory fallacy.
Round three PRO - No positive or negative comments, just arguments.
Round three CON - "Pro concedes..." and "Pro further concedes..." which is another rush-to-declare-victory and by using the term "concedes" falsely suggests that PRO actually conceded the debate.
You make a good point about the simple fact that PRO doesn't type all of the decimal places out explicitly means that they are (de facto) rounding.
1/3 =/= 0.33333(r) without rounding
2/3 =/= 0.66666(r) without rounding
3/3 =/= 0.99999(r) without rounding
All of your efforts to use rounding as examples are moot because PRO already excluded rounding explicitly.
All you have to prove is that PRO requires rounding in order for their case to be true and since PRO already excluded rounding as an option, they have sabotaged their own case.
I view a debate like a basketball game. If your opponent fails to put the ball in the hoop, that does not mean you win automatically. You actually have to put the ball in the hoop. And in my opinion, the best way to do that is with a syllogistic statement that either proves (PRO) or disproves (CON) the debate resolution.
Death23's vote would seem to be invalid because their RFD begins with a long explanation of why they agree with PRO prima facie, which I believe constitutes fabrication of a new argument. They also seem to have misunderstood CON by stating CON requires rounding to make their case.
PRO defeats theirself in round 2 with, "...when you add zero to any number, it equals the number itself. So if the difference between 2 numbers is not zero. They are not equal."
CON's best case was in round 2 with, "Your resolution is impossible because: EITHER - We round and get 1 and/or 3. - OR - We don't round and admit that '7' which is missing in that 0.9recurring * 3 so it can never truly be 3 and thus 3/3 can't be 0.9recurring. Checkmate."
This argument of CON unfortunately fails to address the actual debate resolution, namely "1 and .999 repeating are the same quantity. Exactly equal."
PRO's defense in round 2 of, "Therefore, there is no quantity between 1 and .999 repeating. The difference between them is "zero"." is provably false and this is perfectly clear because of the fact that they had to make a point to quarantine their use of the word zero in quotes explicitly because of what they argued also in round 2 was "If we take 1 and subtract .999 repeating we are quick to say the answer is an infinite set of zeros then a 1. ie .00000..infinity..somehow ends in a 1." which is "virtually zero" and obviously NOT actually zero. PRO uses rounding (between virtually zero and zero) when they already explicitly disqualified rounding.
CON makes what I would consider a mistake in round 3 with, "Pro concedes that..." and "Pro further concedes..."
The use of the term "concedes" is loaded and should be reserved. Also, if CON believes that PRO defeated theirself, a quote would be in order.
0.0001 will always be a quantifiable non-zero difference.
The debate resolution is provably false.
Also, if you add 0.0000(inDEfinite)10000000(r) to 0.9999(inDEfinite)99999999(r) you end up with 1.0000(inDEfinite)999999999(r) which is still not identical to 1.0000(r)
"This equality only applies to numbers ending in point nine repeateing."
By what criteria do you propose that the difference between 1.00000000(r) and 0.9999999999(r) is trivial (AND) the difference between 0.999999999(r) and 0.8888888888888888(r) is non-trivial???????????(r)
I'm not supposed to fabricate arguments when voting.
However, it sounds like Mhykiel needs to support the hypothesis that -
(IFF) 0.99999999999(r) = 1.000000000000(r) (THEN) 1.11111111111111(r) = 1.0000000000000(r) (AND) 0.1111111111111(r) = 0.000000000000000(r) (THEREFORE) 0.11111111111111(r) + 0.99999999999999(r) = 1.111111111111111111(r)
This seems problematic.
For example, (IFF) 0.11111111111111(r) = 0.0000000000000000000(r) (THEN) 0.999999999999999(r) = 0.8888888888888888888(r) (AND) 0.88888888888888888(r) = 0.77777777777777777(r) (THEREFORE) 1.000000000000000(r) = 0.777777777777777777(r)
1) Determinism is incompatible with free-will (an inevitable outcome is not a willful choice).
2) Indeterminism is incompatible with free-will (a random or probabilistic outcome is not a willful choice).
3) No clever mix of the two solve either incompatibility.
First of all, the debate resolution, which is, once again, "1 and .999 repeating are the same quantity. Exactly equal." says absolutely nothing about mathematics or rules or axioms or authority or popularity. So technically, and I do like to get technical, "1" is only one character and ".999 repeating" is fourteen characters including the space, therefore they are not the same quantity of characters and the resolution is technically defeated.
Second of all, for Mhykiel, if you wanted to use google info, you should have made those references explicit within the actual debate. Appealing to a third party will get you nowhere at this point, either make your own case with logic or I remain unconvinced.
And to drafterman, when you say, "All numbers are "finite" because "infinity" isn't a number. The second number would require an [][]infinite number[][] of digits to represent in written form, but we needn't worry about that because we have the [][]appropriate symbols[][] (r) to account for those infinite digits."
How is that substantively different from the idea that "There is an infinitesimal difference of 0.0000(r)1, which is a non-zero value."?
If we have, as you say, "...the appropriate symbols (r) to account for those infinite digits." it does not follow that the symbol referenced "(r)" could not have a number after it or that we couldn't use some other form of notation to identify the infinitesimal.
I'm also not sure how you can say, "infinite number" right after you say, "infinity is not a number".
"Them's the rules" is missing from the debate resolution.
I would cordially like to invite each of you to present your preferred definitions of "infinitesimal" for further examination.
So when you say in round 1,
"1/3 = .333... Repeating
2/3 = .666... Repeating"
You don't mean implicitly "repeating an infinite number of times"?
Do you in fact more precisely mean "repeating an unknown yet finite number of times"?
8/9 is finite.
0.8888(r) is hypothetically infinite.
The difference is "infinite".
While I am willing to grant you they are practically identical, even functionally identical, but they are not perfectly identical.
There is an infinitesimal difference of 0.0000(r)1, which is a non-zero value.
You are making an axiomatic equivocation, which is fine, but logically, this is the same as a bald assertion or an appeal to dogma.
8/9 is finite.
0.8888(r) is hypothetically infinite.
While 0.8888(r) may be a very very very very very very close approximation of 8/9, it is not identical.
It is virtually identical and in practice, practically identical but not perfectly identical.
This is a limitation (flaw) of the decimal system, not a limitation of common fractions.
If the debate resolution was, "9/9 = 1" then I'm absolutely certain there would be no dispute whatsoever.
In order to resolve the disagreement in viewpoints, each side builds a case with logical support.
You begin this process by stating explicit definitions and then addressing any conflicts between the PRO and CON definitions individually as they are identified.
This process is called "identifying common ground".
Once common ground is identified, then a logical case is built by both sides (upon the agreed negotiated definitions) and errors are identified by each opponent.
The point of Civil Debate is to actually resolve conflict and not simply to bully your opponent into submission.
If the definitions are not explicitly agreed upon, then both sides are able to build cases that may use similar words but actually have nothing to do with each other which results in two people talking past each other without realizing they are debating two completely different topics.
8/9 + 1/9 = 1
This was never in dispute when written precisely in this format.
0.8888888888(r) + 0.1111111111111(r) =/= 8/9 + 1/9
The problem identified by PRO (highlighted by the resolution itself) is a limitation (flaw) of the decimal system, not a limitation of common fractions.
This is fundamentally a precision problem.
"...0.8888888888(r) + 0.1111111111111(r) = 0.99999999999999(r)..."
My stated supporting argument directly addresses the debate resolution.
RationalMadman seemed to think that, "Your resolution is impossible because: EITHER We round and get 1 and/or 3. OR We don't round and admit that '7' which is missing in that 0.9recurring * 3 so it can never truly be 3 and thus 3/3 can't be 0.9recurring. Checkmate." closed their case.
However, RationalMadman's argument does not directly address the debate resolution.
The following steel man actually does directly address the debate resolution.
(IFF) 0.8888888888(r) + 0.1111111111111(r) = 0.99999999999999(r) (THEN) 0.99999999999999(r) =/= 1.0000000000(r)
0.99999999999999(r) =/= 1.0000000000(r)
Therefore, "1 and .999 repeating are the same quantity. Exactly equal." is false.
I have no idea why you found my previous comments "annoying and non-productive" since both of these are negative characterizations (ad hominem) and not strictly legitimate objections to my logic.
I really and truly would like to clear up any questions or misunderstandings you or anyone else might have.
Destroying your opponents examples (supporting arguments) alone does not make your case.
That would be like merely blocking your opponent from making a goal.
You actually have to make a goal yourself in order to get a point.
It's called a supporting argument. Supporting arguments are actually integral to the very concept of a debate.
(IFF) 0.8888888888(r) + 0.1111111111111(r) = 0.99999999999999(r) (THEN) 0.99999999999999(r) =/= 1.0000000000(r)
0.99999999999999(r) =/= 1.0000000000(r)
Therefore, "1 and .999 repeating are the same quantity. Exactly equal." is false.
0.8888888888(r) + 0.1111111111111(r) = 0.99999999999999(r) =/= 1.0000000000(r)
Therefore, "1 and .999 repeating are the same quantity. Exactly equal." is false.
If you disagree, please present your argument that disproves my argument or in some other way affirms the debate resolution of "1 and .999 repeating are the same quantity. Exactly equal."
Do you for instance, honestly believe that 0.8888888888888(r) + 0.1111111111111(r) = 1.000000000000(r) ?????????????????(r)
I really and truly would like to clear up any questions or misunderstandings you might have, but at this point you sound like a broken record.
0.8888888888(r) + 0.1111111111111(r) = 0.99999999999999(r) =/= 1.0000000000(r)
Therefore, "1 and .999 repeating are the same quantity. Exactly equal." is false.
0.8888888888(r) + 0.1111111111111(r) =/= 1.0000000000(r)
Therefore, "1 and .999 repeating are the same quantity. Exactly equal." is false.
"...could one infinitely increase the height of the second rock without ever making the second rock 5 feet tall?"
The realistic and very practical answer is no.
There is a practical limit on how many decimal places you can actually type.
Reality is not infinitely divisible. There is a smallest possible unit of space-time.
This would be the Planck length. - https://duckduckgo.com/?q=Planck+length&atb=v79-2&ia=web
Therefore, "1 and .999 repeating are the same quantity. Exactly equal." is false.
When you say, (IFF) "He's not saying that there's a 1 at the "end". He's saying that it's a mistake to think that there's a 1 at the end." (THEN) how do the "9's" ever change? Why don't they stay exactly 0.9999999999999999(r) if there is no way to convert them into anything else?
When I first read debate, I thought of the classic A =/= A argument. However this seems to be a case of A = A.00000000000(r)0000000000001 which is quantifiably false.
Therefore, by PRO's own logic in quote number one, since an infinite set of zeros with a 1 at the end is not exactly and precisely the same as zero, they magically round up to the target value of "1". Because if 1.0 and 0.999(r) were eXactly the same, then the result would obviously be actual zero.
Therefore, "1 and .999 repeating are the same quantity. Exactly equal." is false.
Not to mention 0.8888888888(r) + 0.1111111111111(r) =/= 1.0000000000(r)
This is literally rounding 0.0000(r)0001 to 0.0000(r). PRO stakes their case on rounding. This defeats the debate resolution.
And even if I quote from your previous comment, "Pro's case was that 0.999r must be 1 because 1/3 = 0.333r and 2/3 = .666r and 1/3 + 2/3 = 3/3 = 1. It's a pretty weak case but it doesn't have anything to do with rounding." this is also provably false because 0.333(r) and 0.666(r) approach 1/3 and 2/3 respectively but they require rounding.
Since you can never type out infinite anything, anything ending in an infinite sequence must (EITHER) be typed out explicitly (OR) rounded (like pi).
What PRO actually argued was what PRO said.
And I quote from round 2, (1)"We can confirm this because of the additive identity. identity property of addition, which simply states that when you add zero to any number, it equals the number itself. So if the difference between 2 numbers is not zero. They are not equal."
And I quote again from round 2, (2)"If we take 1 and subtract .999 repeating we are quick to say the answer is an infinite set of zeros then a 1. ie .00000..infinity..somehow ends in a 1. But those zeroes go on for infinity. That singular "1" never appears. Making the answer to what is "1" minus ".999 repeating" equal to an infinite set of zeroes."
Therefore, by PRO's own logic in quote number one, since an infinite set of zeros with a 1 at the end is not exactly and precisely the same as zero, they magically round up to the target value of "1". Because if 1.0 and 0.999(r) were eXactly the same, then the result would obviously be actual zero.
This is literally rounding 0.0000(r)0001 to 0.0000(r). PRO stakes their case on rounding. This defeats the debate resolution.
HOwever, I did not give the "arguments" points to CON because CON failed to clearly identify this error in logic.
You also make a good parallel case, and I applaud your excellent steel man, but I am not fabricating a new argument, I have based my critique on CON's actual statements.
When you said, and I quote from your RFD, "Pro correctly pointed out that no rounding was being supposed.", this statement is provably false.
Please explain what you mean by, "You either learn nothing new or rule one is never broken."
Civil Debate - Rule One: You cannot redefine truth.
Every definition of truth requires facts.
Facts are indisputable.
Just like a court of law, both the prosecution and defense must agree on the facts.
If you and your opponent disagree about a fact, you must immediately stop the debate and negotiate the point of disputed fact.
Civil Debate - Rule Two: Do not disqualify your opponent.
Just like a boxing champion, you are only as good as your opponent.
Ridicule is below the belt.
Use logic.
Your identity cannot qualify or disqualify sound logic.
Civil Debate - Rule Three: Only your opponent can award points.
When your opponent makes a valid objection, you have the option to award them a point.
Valid objections strengthen your argument.
Help your opponent strengthen their position by presenting a steel man.
The best debates are the ones that force you to learn something new.
When Death23 makes the bare assertion, "Pro correctly pointed out that no rounding was being supposed." this is provably false.
What PRO actually argues is that the difference between 1.00000(r) and 0.999999(r) is 0.00000(any number)00000010000(r) which is according to PRO "impossible" and therefore virtually equivalent to zero. However, by notating 0.00000(any number)00000010000(r) it would seem to be no more "impossible" than 0.999999(r) or any other "infinite" sequence (like pi).
0.8888888888(r) + 0.1111111111(r) =/= 1.00000(r)
I would call this a tie on arguments, because CON fails to make a clear case, but I'd consider making a case to award points to PRO for conduct.
Round one PRO - "Hello, I appreciate my challenger taking me up this debate. Good luck to you Sir/Ma'am" which is polite.
Round one CON - "...Pro is tricking you..." which is a negative characterization ad hominem strongly suggesting that PRO is intentionally deceptive.
Round one CON - "'I am smart and good at math'" which is not only a bald assertion but also an indirect ad hominem directed at PRO.
Round two PRO - "Thank you Mad for the quick reply." which is polite.
Round two CON - "You're completely deceiving the reader..." which is a negative characterization ad hominem strongly suggesting that PRO is intentionally deceptive.
Round two CON - "Checkmate." which is a rush-to-declare-victory fallacy.
Round three PRO - No positive or negative comments, just arguments.
Round three CON - "Pro concedes..." and "Pro further concedes..." which is another rush-to-declare-victory and by using the term "concedes" falsely suggests that PRO actually conceded the debate.
Please focus on the debate resolution.
You make a good point about the simple fact that PRO doesn't type all of the decimal places out explicitly means that they are (de facto) rounding.
1/3 =/= 0.33333(r) without rounding
2/3 =/= 0.66666(r) without rounding
3/3 =/= 0.99999(r) without rounding
All of your efforts to use rounding as examples are moot because PRO already excluded rounding explicitly.
All you have to prove is that PRO requires rounding in order for their case to be true and since PRO already excluded rounding as an option, they have sabotaged their own case.
I view a debate like a basketball game. If your opponent fails to put the ball in the hoop, that does not mean you win automatically. You actually have to put the ball in the hoop. And in my opinion, the best way to do that is with a syllogistic statement that either proves (PRO) or disproves (CON) the debate resolution.
3/3=1
0.99999(r) =/= 1
3/3 =/= 0.99999(r)
This is a problem of precision.
Focus on the actual debate resolution and not the supporting arguments.
3/3 is not the debate resolution.
I see a couple of problems.
Death23's vote would seem to be invalid because their RFD begins with a long explanation of why they agree with PRO prima facie, which I believe constitutes fabrication of a new argument. They also seem to have misunderstood CON by stating CON requires rounding to make their case.
PRO defeats theirself in round 2 with, "...when you add zero to any number, it equals the number itself. So if the difference between 2 numbers is not zero. They are not equal."
CON's best case was in round 2 with, "Your resolution is impossible because: EITHER - We round and get 1 and/or 3. - OR - We don't round and admit that '7' which is missing in that 0.9recurring * 3 so it can never truly be 3 and thus 3/3 can't be 0.9recurring. Checkmate."
This argument of CON unfortunately fails to address the actual debate resolution, namely "1 and .999 repeating are the same quantity. Exactly equal."
PRO's defense in round 2 of, "Therefore, there is no quantity between 1 and .999 repeating. The difference between them is "zero"." is provably false and this is perfectly clear because of the fact that they had to make a point to quarantine their use of the word zero in quotes explicitly because of what they argued also in round 2 was "If we take 1 and subtract .999 repeating we are quick to say the answer is an infinite set of zeros then a 1. ie .00000..infinity..somehow ends in a 1." which is "virtually zero" and obviously NOT actually zero. PRO uses rounding (between virtually zero and zero) when they already explicitly disqualified rounding.
CON makes what I would consider a mistake in round 3 with, "Pro concedes that..." and "Pro further concedes..."
The use of the term "concedes" is loaded and should be reserved. Also, if CON believes that PRO defeated theirself, a quote would be in order.
Your question is off-topic.
You seem to have abandoned the debate resolution.
Your question is off-topic.
You seem to have abandoned the debate resolution.
The only way 0.333333333(r) x 3 = 1 is with rounding. PRO already excluded rounding. Case closed.
0.0000(any number of zeroes)000010000000000000000000(r) is not equal to zero.
What we have is a precision problem.
The only way 0.333333333(r) x 3 = 1 is with rounding. PRO already excluded rounding. Case closed.
You wrote, "Because the difference between 1.0000(r) and 0.9999(r) would be 0.0000(r)00001"
0.0000(r)00001 will always be a quantifiable non-zero difference.
0.0000(any)00001 will always be a quantifiable non-zero difference.
What you are describing with your 9/9 and 3/3 examples is a fundamental problem with the base ten decimal system.
We are forced to round up.
Mhykiel already explicitly denied rounding up.
If we were using a base eight system, the problem would happen with eight instead of nine.
If we were using a base sixty system, the problem would be with fifty nine instead of nine.
This is a fundamental problem of accuracy.
It makes no sense to say that the difference between 9 and 10 is somehow less (or less significant) than the difference between 8 and 9.
0.9999 + 0.1111 = 1.1110
0.9999 + 0.0001 = 1.0
0.0001 will always be a quantifiable non-zero difference.
The debate resolution is provably false.
Also, if you add 0.0000(inDEfinite)10000000(r) to 0.9999(inDEfinite)99999999(r) you end up with 1.0000(inDEfinite)999999999(r) which is still not identical to 1.0000(r)
"This equality only applies to numbers ending in point nine repeateing."
By what criteria do you propose that the difference between 1.00000000(r) and 0.9999999999(r) is trivial (AND) the difference between 0.999999999(r) and 0.8888888888888888(r) is non-trivial???????????(r)
Your "proof" should be, The resolution "1 and .999 repeating are the same quantity. Exactly equal." is FALSE prima facie.
There is an obvious 0.111111111111(r) difference which is a non-zero numeric value. End. Of. Story.
I'm not supposed to fabricate arguments when voting.
However, it sounds like Mhykiel needs to support the hypothesis that -
(IFF) 0.99999999999(r) = 1.000000000000(r) (THEN) 1.11111111111111(r) = 1.0000000000000(r) (AND) 0.1111111111111(r) = 0.000000000000000(r) (THEREFORE) 0.11111111111111(r) + 0.99999999999999(r) = 1.111111111111111111(r)
This seems problematic.
For example, (IFF) 0.11111111111111(r) = 0.0000000000000000000(r) (THEN) 0.999999999999999(r) = 0.8888888888888888888(r) (AND) 0.88888888888888888(r) = 0.77777777777777777(r) (THEREFORE) 1.000000000000000(r) = 0.777777777777777777(r)
I'd suggest, "free will" is defined as "the capacity to make a decision that is free of all previous influence".
The Standard Argument Against Free-Will (TSAAFW)
1) Determinism is incompatible with free-will (an inevitable outcome is not a willful choice).
2) Indeterminism is incompatible with free-will (a random or probabilistic outcome is not a willful choice).
3) No clever mix of the two solve either incompatibility.
Therefore, free-will is an incoherent concept.