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0.9999.... is equal to 1

Name: Krieger 2008-08-29 2:44

I honestly thought that by this time, everyone in the world knew this was true, save those who have absolutely no idea what numbers are.....ok, I'll do my best to explain this to all you would-be trolls.

1/3 = 0.333
now multiply both sides by 3 and you get:
3/3 = 0.9999....
OR
1 = 0.9999....

Now, Let's start with 1 = 0.99999.... this time.
Subtract 0.9999.... from each side and you get:
0 = 0.00000....
Yes, there is a 1 there, but it is exactly aleph null zeros from the decimal.....meaning it kinda isn't there, and that you just subtracted the same number from two numbers and got the same answer for both....thus they must be equal.

Last: between any two unequal real numbers, there are infinitely many numbers. I'd like to challenge anyone to find a number between 0.9999..... and 1. If you can find that number, then you win infinitely many internets, but if not, just admit that 0.999... does, in fact, equal 1.

Name: Krieger 2008-09-01 21:46

>>8
Assuming that 0.00...1 actually made sense, 1 - 0.0....1 would be the same as 0.999...

>>12
If 0.999.... is equal to 1, then it would be 1, if not, it would be 1.000.....1, another nonsensical number.

I think it would help a lot of people if they knew the properties of infinity. Let's say you have a line (or a ray, line segment, whatever you wanna call it), originating at one point and proceeding in one direction for an infinite distance (let's say aleph null distance). If you're standing at the origin, the end of this line wouldn't just be a very long distance away, because a "very long distance" suggests that if you go a very long time, you'll get there. You will never get to the end of this line, because it is never there. Now, let's replace the origin with 1. and the line with a string of zeros. At the "end" of this string of zeros is a one. The problem is, you can never get to that 1. If something can never be reached, has never really been seen, and who's position has been identified as being the same as an imaginary entity's position (the end of infinity), then is it truly there? I say no, the vast majority of the mathematical community says no, and you should say no.

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