https://old.reddit.com/r/confidentlyincorrect/comments/1b0iycz/999repeating_does_in_fact_equal_1/
!math !mathematics nerd slapfights
https://medium.com/@kenahlstrom/proof-that-99999-is-not-equal-to-1-5672e7dd58ce
Another day of Redditors being confused by high school math. Although to be fair, I still think proportionally the number of people who get it here is still higher than the general population.
I had meant for that to sound encouraging, but in hindsight actually that's terrifying.
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.9(9) can only refer to limit as n approaches inf of the partial summation
^n _{i=1} 9/10^i. This limit is identical to 1. Colloquially, the difference between .9(9) and 1 is smaller than any positive (thx iceberg) number you could come up with
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1/3 = 0.33333...
1/3+1/3+1/3=0.333...+0.333...+0.333...=0.999... = 3/3 = 1
0.999... = 1
Only literal
argue this
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you'll need to justify this definition with the infinite threes. further, you have to justify why you can add these infinite decimal expansions. while your argument may be convincing to elementary/high school students, those subtleties are addressed in real analysis and my above outline of a
proof
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I don't have to do shit, actually. Suck me.
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come here babe
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Also it's literally long division and addition of two real numbers, it could convince an elementary school student. Pardon me for not starting from axioms. Frick.
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It's true that 0.9999… = 1, but this "proof" is begging the question by asserting that 1/3 = 0.3333….
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My calculator says so
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https://rdrama.net/h/nerdshit/post/292051/0999-or-1-redditard-debate-soysnooseethe/6854134#context
Lol
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I have an oddly relevant comment, one moment
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Isn't this just a result of base 10 being gay and r-slurred for decimals
We should just use fractions for everything, including programming
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It's the result of real analysis being gay and r-slurred (but important and usable)
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Almost every number cannot be represented by a fraction smdh
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Imperial units gang rise up, and decapitate the metricels
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lmao, fractions are r-slurred.
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Nuh uh, the difference is not smaller than zero, which is a number. Checkmate!
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UCK FRICK FRICK IM RUINED
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The limit does not exist,
In the ten-adic topology.
So the question really depends on a whole bunch of unstated assumptions, like using the usual topology instead of the 10-adic topology.
What is fun is tripping people up by asking if you can have different sizes of infinities of nines. Since popmath people like saying that there are different sizes of infinity.
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well isnt there like an infinite amount of real numbers between any two integers, so like the amount of real numbers from 0 to infinity is like inifinity times more than the number of integers from zero to infinity?
although calculus 101 suggests that I cant just compare infinities directly and instead compare the function that produces them, like l'hoptial's.
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there are also infinitely rationals between two integers but rationals are countable just like integers.
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The latter case is called "uncountably infinite" because it isn't possible (IIRC) to map natural numbers to the set of real numbers. I like to think of it as a sort of fractal infinity -- that anywhere you look is another infinity within an infinity (etc.).
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Hospitallers
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Lmao I was considering saying" in the real numbers with the usual norm etc" but then though no way there's some pedantic neurodivergent going to
me
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10-adic is nonsensical because 10 isn't prime
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You may be right that the ring is nonsense, because the limit very much does not exist because not even 1/10 exists without the nice field of fractions. lol.
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The real numbers are often constructed as the equivalence classes of Cauchy sequences of rational numbers so in an extremely precise sense it's completely correct to say that ".9999…" (defined as the obvious Cauchy sequence) indeed equals "1.000…" similarly defined.
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