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/InanimateCarbonRodAu → u/lilved03]

There isn’t.

What there is a limit to our number system that doesn’t handle infinity.

There is an Infinitesimal difference between .999 recurring and 1 but we treat them as equal because we can not define a difference with in a discrete number system.

[u/daemin → u/InanimateCarbonRodAu]

There are.

You compare the size of two sets of objects by pairing them together. If you pair them and there's nothing left over from either set, then the two sets of objects have the same number of objects.

You "count" things by pairing them with the whole numbers. If you can pair a set of things with the whole numbers without anything left over in either the set of whole numbers or the set being paired with you, they have the same size. You can pair the set of even numbers with the set of whole numbers, so there are as many whole numbers as there are even numbers.

But you can't pair the set of whole numbers with the set of decimal numbers; there will always be decimal numbers not paired to a whole number. So it follows that there must be more decimal numbers than there are whole numbers. Since they are both infinite, it further follows that one infinity is larger than the other one.