luiaots said:
pezus said:
walsufnir said:
pezus said:
MDMAlliance said:
Talal said:
Not to sound arrogant, but it's a pretty established fact that 0.999.. equals 1.
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I think we're using the word "fact" wrong if it is contested. In pretty much any math equation you will ever come by, it will equal 1. However, it is not a fact that .999... itself is actually 1. Every time I see someone trying to prove it, it keeps showing me that they are either using circular logic, or are approximating, then claiming they are the same thing.
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It is a fact and can be easily proven in many ways. One of the ways was in the OP last I checked.
x = 0.999...
10x = 9.999...
10x-x = 9.999...-0.999...
9x = 9
x = 1
And therefore: 0.999... = 1
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I call this invalid as you can't really subtract infinite nu,bers from another. If you subtract it has to be a finite number.
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But that's the thing, I am not subtracting infinite numbers from another.
Here's another proof from Wikipedia:
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If you couldn't subtract "infinite" numbers ( wrong use of the word, you dont mean infinity, you mean numbers whose decimal expression doesn't end) then you couldnt add or subtract pi, e, or most fractions from anything.
Edit: For example, you couldnt do .666666... -.3333333..., but we can, since we can write it as 2/3-1/3=1/3
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It depends on your representation. Of course I can subtract ratios but in this special case we subtract the decimal presentation of periodic numbers which is definitely different to pi.
