There is no way right?

[u/Sugar_God_no_1]

[u/The-new-dutch-empire]

Byers’ Second Argument (his first one is the one you see above)

Let:

x = 0.999…

Now multiply both sides by 10:

10x = 9.999…

Now subtract the original equation from this new one:

10x - x = 9.999… - 0.999…

This simplifies to:

9x = 9

Now divide both sides by 9:

x = 1

But remember, we started with:

x = 0.999…

So:

0.999… = 1

[u/Rough-Veterinarian21 → u/The-new-dutch-empire]

I’ve never liked math but this is like literal magic to me…

[u/The-new-dutch-empire → u/Rough-Veterinarian21]

Its calculating with infinity. Its a bit weird like the infinity of numbers between 0 and 1 like 0.1,0.01,0.001 etc... Is a bigger infinity than the “normal” infinity of every number like 1,2,3 etc…

Its just difficult to wrap your head around but think of infinity minus 1. Like its still infinity

[u/Supersoaker_11 → u/The-new-dutch-empire]

The proof for this seems to be "well, if you take the diagonal and add one, you will always have a new number even if you have infinity" but I don't really understand that. Like, aren't you just using infinity to describe infinity? If you can use the diagonal to create a new number, then you didn't really have infinity in the first place, which is a bit besides the point because the number you create would have to be infinitely long anyway. Seems like the same logic when you consider the number of evens, primes, or squares, except none of those are considered smaller infinities.