Proof: 0.9999 does not equal 1

[Math401]

Or rather counter proof.
They said x=0.999...
10x=9.999...
9x=9.999...-x
9x=9
x=1
but this is obviously wrong, you can't substract infinity from infinity unless you consider infinity a number and if so then you would get 8.99...1 and not 9. either way 0.999...= 1 is wrong. and is not different than saying (0.999...) +x=1.99...8 you can't add an infine amount of nines to an infinite amount of nines or subtract. if you could then you would consider infinity as a number and in that case the proof is also wrong

 

[DrClaude]

This subject has been discussed many times on PhysicsForums. Please do a search of the forum or look at the "Similar Discussions" links below.

Yes, 0.999... = 1.

0.999... = 1 because, by the definition of "decimal place notation", 0.999... is the limit of the infinite series .9+ .09+ .009+ ... That's a geometric series and it's easy to show that the limit is 1.

Thread closed.

 

[Mark44]

but this is obviously wrong, you can't substract infinity from infinity

We are not subtracting infinity from infinity here. The subtraction is 9.999... - 0.999..., with each number having an infinite number of 9 digits to the right of the decimal point. The result is 9.000..., with an infinite number of 0 digits to the right of the decimal point.
As DrClaude said, this has been discussed many times here at PF.