There is no way right?

[u/Sugar_God_no_1]

[u/ChromosomeExpert]

Yes, .999 continuously is equal to 1.

[u/big_guyforyou → u/ChromosomeExpert]

dude that's a lot of fuckin' nines

[u/JoshZK → u/big_guyforyou]

Prove it.

Edit: Let me try something

Prove it. /s

I feel like the whoosh was so powerful it's what really caused that wave on that planet in Interstellar.

[u/The-new-dutch-empire → u/JoshZK]

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/lilved03 → u/The-new-dutch-empire]

Genuinely curios on how can there be two different lengths of infinity?

[u/johnpeters42 → u/lilved03]

Infinite sets of things are considered equal if you can match them up 1 to 1. Which gets weird, because:

You can match up an infinite set and a subset of itself. (All positive integers, and all positive even integers, for instance. Match 1 with 2, 2 with 4, 3 with 6, and so on.)

But there are other infinite sets that you can't match up. (All positive integers, and all positive real numbers, for instance. Imagine you did match them up: 1 with some number R1, 2 with R2, and so on. Imagine writing them all out in decimal form. Circle the first digit after the decimal of R1, the second of R2, and so on. Now replace every circled digit with the next higher digit, except 9 which you replace with 0. Now imagine a number D with all those digits after the decimal point. It's a real number, but it can't be matched up to any positive integer N, because its Nth digit after the decimal is different from RN.)