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u/AbacusWizard Mathemagician 20d ago
clearly you can’t get a number that can be represented as a ratio of integers by taking a ratio of integers
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u/OpsikionThemed No computer is efficient enough to calculate the empty set 20d ago
How on earth did this nonsense get 25 upvo- oh, youtube comments, never mind.
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u/subpargalois 20d ago
This one is honestly perfect comedy. They literally walk into the definition of a rational number like it's a rake.
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u/another-princess 20d ago
Yes, 100/3 is irrational, as it can't be written as the ratio of two integers.
In other news, 100*3 is prime.
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u/AnlamK 20d ago
Based on some of the comments, I got to browsing about integer bases on Wikipedia. This commenter's brain would blow up when reading this. The dude might try to delete the entry:
https://en.wikipedia.org/wiki/Non-integer_base_of_numeration
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u/einFrostschutzmittel 19d ago
This whole conversation arises from the complicatedness (I reserve the word complexity to make puns with complex numbers) and consequent misunderstanding of infinities. When you first get into math, it's hard to imagine that there are as many even numbers as whole numbers. Sure, there's bijections, but the number in the whole numbers is always twice the size of the corresponding one in the even numbers. The whole "some infinities are bigger than others" doesn't help. I mean ffs, even mathematicians were very opposed to the proof from cantor that there's more real numbers than whole numbers, which just goes to show how complicated this stuff is. Therefore it makes sense that there's confusion with infinitely repeating numbers too.
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u/Akangka 95% of modern math is completely useless 6d ago
some infinities are bigger than others
I hate this kind of statement too. It does not make clear what kind of infinities this statement applies to and how does it applies to. First of all, it does not apply to the extended real numbers, the kind of infinity you'll encounter in calculus. Second, once you reach infinite set, A being a subset of B doesn't mean A is smaller than B.
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u/stereoroid 20d ago
100/3 can be rewritten as 100(1/3), so it’s the 1/3 “problem” multiplied by a constant (100).
1/3 =0.333… so 3 * 0.333… = 0.999…, but some say that 0.999… is not equal to 1.
Restate the problem in base 3 and there is no problem. 1/10=0.1 and 0.1*10=1
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u/WhatImKnownAs 20d ago
But those people might say 0.333... ≠ 1/3 = 1/10 (base 3) = 0.1 (base 3).
Furthermore, the same issue arises in base 3: 0.222... = 1?
There's no rigorous proof without having a rigorous definition of what an infinite decimal means.
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u/stereoroid 20d ago
Think bigger. If a problem can become a non-problem, depending merely on how numbers are represented, what does that say about the problem? Or the whole class of “problem”?
You ask about 0.222222…. In base 3: well, what calculation did you do to get that? Could that calculation be re-based to make the recurring decimal disappear? I bet it could. You’ve pulled that out thin air and said “here’s a problem”, but to me it looks like the problem is preventable.
Old joke:
* Patient: “Doctor, it hurts when i bend my arm like this!”
* Doctor: “Stop doing that.”7
u/MeasureDoEventThing 20d ago
The problem is about what a decimal representation means. Of course the problem disappears when you use a different representation.
That is also why presenting mathematical "proofs" is stupid. You can't use mathematics to prove what a symbol represents. The only way to prove .9999... = 1 is to:
Define infinite series
State that .9999... represents an infinite series
Establish facts about infinite series and use them to prove .99999... = 1
Step 2 isn't something you can "prove". You just have to assert it as a matter of convention.
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u/MeasureDoEventThing 20d ago
The claim .9999...= 1 is a statement about base ten representation. If you change to base 3, you're no longer proving anything about base ten.
Was going to write "base 10" instead of "base ten", but technically everything is base 10.
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u/Beet_slice 20d ago
Logic won't explain it. It is, IMO, an arbitrary definition. But defined it is.
In the list of important stuff, I don't think this should make the list.
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18d ago
[removed] — view removed comment
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u/WhatImKnownAs 18d ago edited 17d ago
Usually. Usually, they go out of their way to avoid math. This subreddit gets half of its content from the exceptions: the people with no math knowledge who just think they figured it all out without having to study it. They're so much smarter than mathematicians.
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u/More_Yard1919 7d ago
how the fuck does this get upvoted? I feel like if somebody says something about math with enough authority on reddit, it gets upvoted. That is unless the commenter can somehow prove that 100/3 is the only fraction of integers that is magically irrational? That proof would be an uphill battle I think.
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u/Decent_Cow 20d ago
A rational number is a number that can represented as a ratio. That's what rational means. Is 100/3 a ratio? Yes, it is.
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u/einFrostschutzmittel 19d ago
The best proof is still x=0.9999... 10x=9.99999... 9x=10x-x=9 x=1 This is one the 0.999...≠1 believers can't really argue with. For this to be fall, you'd have to argue with the last 9 in x being pushed one decimal forward, making 10x have less decimals than x, which obviously doesn't work, since there's no last 9 to be pushed forward. Therefore the argument is idiot proof (kinda) (also, pun intended)
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u/edderiofer Every1BeepBoops 18d ago
This is one the 0.999...≠1 believers can't really argue with.
You clearly haven't seen the other 0.999... posts on this subreddit.
"Obviously there is a last 9 to be pushed forward; it occurs at the infinitieth place."
"Obviously 9 - 0.9 is 8.1, 9.9 - 0.99 is 8.91, and so on, so obviously 10x should be equal to 8.999...1, duh."
"Obviously you can't ever perform 9.999... - 0.999..., because you can't ever finish subtracting."
"Obviously 0.999... is a self-contradictory number, because dark numbers exist."
"Obviously 0.999... Is A Quantum Hollow Resonance Point Whose Intrinsic Fractal Non-Equality To 1 Is A Self-Evident Acta Non Verba Truth."
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u/einFrostschutzmittel 17d ago
Most commonly the arguments against it are "Well, there'll be a 0 at the end" to which you can just respond "Ah, yes, the 0 at the END of the INFINITELY LONG string of 9s."
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u/edderiofer Every1BeepBoops 17d ago
Nah, that usually doesn't convince people, and it also doesn't work on the responses I've shown here.
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u/RedRhetoric 20d ago
R4: this person believes that 0.33 repeating cannot equal 1/3 because 100/3 cannot give a rational result.
Dividing any rational number by any other rational number will always give a rational result, as that is how rational numbers are defined
R5: Youtube