0.999... = 1
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0.999... = 1: Prove that 0.999 (repeating to infinity) isn't equal to 1.
x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1
0.333... = 1/3
0.666... = 2/3
0.999... = 3/3 = 1
All numbers that aren't equal to each other will have a number(s) that comes in between.
x < x+1 --- The number that could come in between of x and x+1 could be x+1/2.
So, give a number that comes in between 0.999... and 1.
You (as Con) will try to prove 0.999... (repeating to infinity) IS NOT EQUAL TO 1.
And don’t even try to disprove 1 because it’s impossible.
All numbers that aren't equal to each other will have a number(s) that comes in between.x < x+1 --- The number that could come in between of x and x+1 could be x+1/2.So, give a number that comes in between 0.999... and 1.
The number in the middle is 0.999... with a '05' at the end. Similarly 0.999... itself has a '9' at the end that is meant to also theoretically be followed by infinite 0's (since all numbers have that following and the infinite 9's must end in a 9) so it's just as impossible of a value as the midpoint between it and 1.0000...
The difference between 0.999... and 1.000... either exists or 0.999... doesn't exist at all numerically and therefore it can't be equal to 1.
I'm simply warning you that arguments like the last two rounds will not win you this debate
There. And since 0.999... is equal to 1, I have reversed engineered it. While it may not look like 0.999...
0.999...995 < 0.999...
The hand-waving is obvious. How does one multiply an infinite series of 9s by 10? What happens to the zero you’d get when multiplying by ten? Are we to believe it just disappears?.999=x10x=9.99910x – x = 9x9x=91x=1..999 = 1.
Of course not. The proof is invalid. It’s just an optical illusion relying on tricking the reader by hoping they don’t notice the hand-waving. The reality is no “proof” can address the issue better than simply looking at the two values. If the two are equal to one another, subtracting one from the other must give an answer of 0.
When we do that, we see there is a difference – 0.000…1. It’s infinitely small, but it is real. Therefore, the two numbers aren’t equal. Why then do so many people believe they are? Because they say so.
Literally. They say so, so it’s true. That’s it. You see, there is a thing in math called an axiom. It’s a statement assumed to be true without proof. One axiom underlying the real number system basically says:Non-zero infinitesimals do not exist.Which means 0.000…1 does not exist. Why? Because we say so.
Only we don’t say so. A person who thinks 0.999… doesn’t equal 1 obviously believes infinitesimals exist. They don’t accept that axiom. They’d use a different one, like many mathematicians who work with infinitesimals on a regular basis.
That’s right. There’s an entire field of math which uses infinitesimals. It’s just as valid as the real number system. Which one you use is merely a matter of preference. Whether 0.999… and 1 are equal is based on the completely arbitrary choice of whether one uses the real number system or a different one.
All the “proofs” the two are equal are meaningless. Implicit in all of them is the statement, “Using the real number system.” That’s begging the question. It’s tricking people by assuming there could be no difference between the two numbers then concluding there is no difference between the two numbers.
Anyone who understands how math works should know 0.999… equals 1 only if you choose for it to. “Proofs” the two are equal tell us nothing about the subject but everything about the speaker. Namely, they don’t know what they’re talking about.If you feel 0.999… does not equal 1, you’re right. If you feel it does equal one, you’re right too. Which answer is “right” just depends on which type of math you feel most comfortable with. It’s purely a matter of personal choice.