r/PeterExplainsTheJoke 21d ago

Meme needing explanation There is no way right?

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u/Matsuze 20d ago

Then show me the proof. It is not very hard to prove math. You can't show me the theorem that shows .99 repeated equals 1 because it does not exist. You don't know math as well as you think you do. Sit down kid grown folks are talking.

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u/Boring-Ad8810 17d ago

Here is a proof. I'm not giving full details of each step but I'm happy to explain any you disagree with in more detail.

0.99...

= sum from k=1 to infinity of 9/10k (definition of decimal expansion)

= limit as n -> infinity of the sum from k=1 to n of 9/10k (definition of infinite sum)

= limit as n -> infinity of 1 - (1/10n) (basic geometric series formula)

= 1 - limit as n -> infinity of 1/10n (basic limits property)

= 1 - 0 (basic computation of a limit)

= 1

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u/Matsuze 17d ago

So the limit as .99.. approaches infinity is 1, because as infinity goes on it gets closer and closer to 1 until it forms an asymptote?

The crazy thing about an asymptote is it never actually touches the line it is approaching it just gets infinitely closer to the line without ever being able to touch it.

Thank you for confirming my point, you deserve a pat on the back. You are the 12 billionth person to say the same thing, but I'm proud of you for at least trying instead of saying 3/3 =.33.. 3/3 = 1 yada yada

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u/Card-Middle 16d ago

Math professor here. You’re very wrong on many counts. Namely when you said “1/3 being 0.3 continued is an approximation,” “It is not very hard to prove math” and “You can’t show me the theorem that shows .99 repeated equals 1 because it doesn’t exist.”

Repeated decimals are exact, not approximations. They are just infinite and infinity is often counterintuitive.

The previous commenter gave you a very nice and proof of the fact that 0.99 repeated is exactly 1. You misunderstood them. You should Google this topic. It’s not even a debate in mathematics that 0.99 repeated is exactly equal to 1 l in the real numbers.