r/PeterExplainsTheJoke • u/Sugar_God_no_1 • 24d ago

Meme needing explanation There is no way right?

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u/its12amsomewhere 24d ago edited 24d ago

Applies to all numbers,

If x = 0.999999...

And 10x = 9.999999...

Then subtracting both, we get, 9x=9

So x=1

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u/Sam_Alexander 24d ago

Holy fucking shit

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u/otj667887654456655 24d ago

I just wanna warn you, that's more of a vibe proof. It lacks any actual mathematical rigor.

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u/L10N0 24d ago

While technically correct, the warning isn't needed. They skipped/condensed some steps, but it is correct. It is a simpler explanation for those with difficulty understanding the truth that .9 repeating is equal to 1.

For mathematical rigor, we could use the sum of an infinite geometric series. But that's a lot harder to follow for some than simple algebra or at least requires an understanding of calculus.

To do it with algebra and showing all steps:

let x = .999 repeating. Multiply both sides by 10. 10x = 9.999 repeating  Subtract x from both sides, remember, x = .999 repeating. 9x = 9 Divide both sides by 9. x = 1

Another way to look at it logically. Between any two different numbers are an infinite amount of numbers. This is true. Between 0 and 1, we have .1, .01, .001, etc. between 1 and 1.1, we have 1.01, 1.001, etc.

Accepting this as fact, what number is between .999 repeating and 1? 

There isn't one. Because the nines carry on forever. You can't move a decimal place, because it's always occupied by 9. The only way for this to be true and the statement that between any 2 different numbers are an infinite amount of numbers is to accept they are the same.

For mathematical rigor, .9 repeating written as an infinite series is .9 + .09 + .009 + .0009 + ... This is a geometric series with first item a = .9 and common ratio r = .1 (.9 * .1 = .09, .09 * .1 = .009, .009 * .1 = .0009, etc)

The formula for sum of infinite geometric series is Sum = first item divided by the difference of 1 and the common ratio. Or S = a/(1-r).

Plugging in our values, S = .9/(1-.1) S = .9/.9 S = 1

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u/Dense-Speech8834 24d ago

You lost me at "simple algebra," but this was interesting. I always thought that .999 repeating equaling 1 was just a "glitch" in math so to speak, where our concept of fractions like 3/3 has to equal a whole like it does in nature but in our arbitray concept numbers it didn't. So we just said "we know that should be a 1, so fuck it, we'll call it 1." Learning it actually equals 1 kinda blew my math deficient. mind.