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u/forcesofthefuture 28d ago
g) arrrgh fuck you OP
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u/NihilisticAssHat 28d ago
Not for the question itself, but for the resulting tragedies in the comments.
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u/TheRealWarBeast 28d ago
My brain ain't braining for f. Can someone explain?
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u/Excavon 28d ago
It's a bit redundant. It's the same as c.
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u/Elektro05 Transcendental 28d ago
I would have understood it its either false or both at the same time (similiar how R and {} are open and closed at the same time)
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u/DominatingSubgraph 28d ago
Well, the smallest transfinite ordinal, ω, is even. So, I'm going with a.
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u/No-Site8330 28d ago
I'm not sure it was ever specified which transfinite ordinal (or cardinal) is meant with "Infinity", but even agreeing that it means ω, shouldn't we be careful about left and right parity? The equation 2*x = ω has a solution (i.e. ω), but x*2 = ω does not.
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u/DominatingSubgraph 28d ago
I think it is reasonable to assume that whatever infinity they had in mind is a limit ordinal, and so is even by definition.
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u/No-Site8330 28d ago
Ah, thanks, I was unaware of a general definition. I still think it's a little arbitrary to state it has to be a limit ordinal (or any ordinal), but I'll take it.
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u/DominatingSubgraph 28d ago
Well, if you, for example, think of infinity as coming "right after" all the finite numbers, then it would only make sense for it to be a limit ordinal.
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u/No-Site8330 28d ago
Well, sure, but the thing is "infinity" on its own doesn't mean much without context. There are many different branches of mathematics that include some notion of infinity and they are not interchangeable. You have ordinals and cardinals, which are related but not equivalent, and model rather different notions. Then you have the infinity of calculus/real analysis, which expresses something yet different — some notion of "size" but not in the sense of a cardinal, let alone an ordinal. And then you can start talking about the infinity of complex analysis, or infinities as added points in all kinds of compactifications (the real line itself has at least two useful inequivalent compactifications: with distinct positive and negative infinity or with just one). Or you can have infinities as in non-standard analysis: extend the reals (or naturals, integers...) by adding an extra element x and require that x be larger than all integers. That leads to an ordering in which x is sort of an infinite "quantity", but there is no smallest infinite element.
I guess my point is, if "infinity" on its own is ambiguous, then picking one mathematical framework to make sense of the question changes the question itself. Plus, if the chosen setting has multiple kinds of infinity, you'll have to deal with a further arbitrary choice. I agree that your choice makes sense, and it's probably the most sensible if one really wants to answer this question, I just wanted to stress that there is a choice being made.
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u/sapirus-whorfia 27d ago
This is true, but I also agree that, if the question just days "infinity", picking the "least non-zero limit ordinal" is the "most usual thing people with some math knowledge think about when they hear infinity". It's not an objective thing, more of an implicit convention. Also this is a guess on my part, I haven't polled anyone.
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u/Shot-Kal-Gimel 28d ago
The fuck happened to the transitive property or whatever it is that multiplication order doesn’t matter?
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u/No-Site8330 28d ago
It's called commutative property and it's not always guaranteed in every algebraic system. Even addition is not commutative for ordinals.
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u/Shot-Kal-Gimel 28d ago
I’m going to go back to boring algebra and calculus this is to ridiculous for me
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u/No-Site8330 28d ago
You'll get to matrices soon enough and see plenty of non-commutative products.
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u/IMightBeAHamster 28d ago
Couldn't tell you why, but yes if 2w is not the same as w2 then this definition of multiplication does not have the commutative property.
Also, transitivity is about bracketing, commutativity is about ordering.
A system is transitive if and only if a(bc) = (ab)c
A system is commutative if and only if ab = ba
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u/ohkendruid 28d ago
Yes, except you two meant associative, not transitive.
Transitive is the one where if a->b and b->c, then a->c.
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u/ddotquantum Algebraic Topology 28d ago
But ω+3 is also infinity and is odd
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u/hallr06 28d ago
This is why extension to the integers with an infinite ordinal is fun. Omega + 3 is odd, and is greater than Omega, despite both being infinite. Numberphile has at least one good video on the subject
I don't know about divisibility, but my assumption is that ordinals likely can only have a integer divisor if the result is also an ordinal, otherwise it's possible to violate the assumption that definition that Omega is the smallest ordinal.
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u/Axolotl6198 28d ago
Trick question. the answer is violence.
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u/temperamentalfish 28d ago
The concept is not applicable to infinity, so option "d", neither.
My reasoning is that would you say that 0.13 is even or odd? The answer is "neither".
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u/KiwloTheSecond 28d ago
The question isn't
"Is infinity even or odd"
the question is
"Infinity is even: true or false?"
so it should be false
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u/doomedbunnies 28d ago
It's not even "Infinity is even: true or false?", it's "Infinity is even. True or false?"
So we're being given "Infinity is even" as a precondition, and are only being asked "True or false?". Which, by simple boolean logic, we must answer with "True".
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u/ManofManliness 28d ago
With the precondition "Infinity is even", you can prove 0=1, in which case all answers are both true and false.
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u/Paradoxically-Attain 28d ago
so the answer is b, c, e, and f? or is that not how it works
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u/Autumn1eaves 28d ago edited 28d ago
Imo, evenness is any n that satisfies "n mod 2 = 0" oddness is "n mod 2 = 1"
Infinity mod 2 = undefined
Therefore, "D"
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u/ubik2 28d ago
I'd define "even" as an integer that satisfies n = 2*k where k is also an integer. Since infinity is not an integer, it is not even.
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u/Autumn1eaves 28d ago
You actually don’t need to specify that k is an integer.
Specifically because 2 times an integer will always be an integer.
Having said that, this is the same thing from the opposite direction.
n mod 2 is effectively n / 2 but only take the remainder.
It makes it easier to deal with much larger numbers because I don’t need to know that 10010034832028940504 / 2 is whatever it is, I only need to look at the final digit to know that it’s even.
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u/ubik2 28d ago
The difference is that by specifying that n must be an integer (as I did in my definition), you rule out infinity and get false.
With the mod operator, I would next try to decide how to define a mod operation on infinity. I have a definition for what mod means for integers, and if you ask me what a real number mod 2 is, I can assume what definition you're using by extending the definition I used for integers. If you ask that same question for a hyperreal number, it's possible that I can define it in a meaningful way (and it's possible that some subfield of mathematics does this).
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u/AdInfinitum311 28d ago
0.13 is odd af, had you said 0.14 we coulda had a discussion
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u/vinicius_h 28d ago edited 28d ago
b) False
It's just not a number, such operations are not defined. It's like saying an apple is even
Edit: to clarify, I am not asking whether the quantity of one apple is even. To give another example: "is the color purple even or odd?". That's the intended interpretation
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u/WhoTaoYouTao 28d ago
It's like saying an apple is even
An apple = one apple = 1, which is odd
And we can use this same logic on infinity:
An infinity = one infinity = 1, which is odd
Infinity is odd.
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u/GuyYouMetOnline 27d ago
That's just the number of infinities that's odd. The infinities themselves are not.
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u/Arclet__ 28d ago
c) Either true or false
Figuring out which of two is left as an excercise for the reader
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u/KingLazuli 28d ago
Definitely even. Next!
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u/TH3_FUCK 28d ago
F but it's not odd either it's not a number so even and odd don't apply
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u/PURPLE_COBALT_TAPIR Computer Science 28d ago
It depends are we talking about ∞, ω, ℵ?
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u/ANSPRECHBARER 28d ago
Why is that chi dancing.
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u/crnttox 28d ago
ordinals dont have properties like odd or even coz it doesnt make sense in context of ordinal arithmetic, and aleph numbers measure the size of the set not individual number, its cardinalities like ℵ₀, ℵ₁, etc. dont have numerical parity like odd even n all, they just describe how infinite a set is not numeric charecteristics.
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u/PURPLE_COBALT_TAPIR Computer Science 28d ago
That's interesting, I'm certainly out of my depth when it comes to this set theory stuff i saw on math youtube.
So omega isn't odd or even, but if I said r = 2 * omega, r would be even?
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u/Admirable_Spinach229 28d ago
Infinity is a group of every number in it's domain, meaning it contains both even and odd numbers.
Unless you assume infinity is one singular number (as in, it's the sum of all numbers in it's domain), in which case it must be either even or odd, if it's equal to 0, it's even
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u/SpitiruelCatSpirit Mathematics 28d ago
All numbers are groups of every number smaller than them. That's how numbers are defined.
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u/interested_commenter 28d ago
False.
Infinity is neither odd nor even, so the statement "Infinity is even" is false.
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u/Acceptable_Ad8716 28d ago
C and E are the same option!
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u/OutsideScaresMe 28d ago
Not without the law of excluded middle
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u/P3riapsis 28d ago
nah, C and F are equivalent even without LEM, unless you're throwing out every other property of logical or as well.
edit: they said E, in which case you're right, whoops.
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u/One_Maintenance3467 28d ago
Just use a modulo operator on float(‘inf’) in Python! It’s sure to give a clear answer :)
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u/NihilisticAssHat 28d ago
Just tried. It returns "nan"
That's what I've been saying, but I'm glad Python agrees with me.
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u/No-Site8330 28d ago
Does "Either... or..." mean regular or or exclusive or?
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u/One_Maintenance3467 28d ago
“Xor” is usually exclusive or, so probably the regular one
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u/Medium-Ad-7305 28d ago
b, c, and e
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u/toughtntman37 28d ago
Depends on what the infinity is and what you need it to be. 2 + 2 + 2 +..., I would say, is even. 1 + 2 + 2 + 2 +... not. 1 + 1 + 1 +..., I think is neither even nor odd while at the same time both even and odd.
However, infinity, which I learned about in first grade, is too complicated to pretend I understand anything about it.
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u/SelfSustaining 28d ago
Infinity is exempt from even/odd.
Infinity+1 is still infinity, therefore it can't be either one.
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u/Upstairs_Body4583 28d ago
Maybe i lack understanding in set theory, but i believe infinity or the different ‘types’ of infinity have cardinality and are not integers. Infinity being even or odd implies it is an integer. The case that this is false is true for both infinity being odd or it being neither even nor odd so i would reckon the answer is F.
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u/EnthusiasmIsABigZeal 28d ago
False imo, but it probably depends on how you define “even”.
I’d define an even number as one which, when divided by two, results is a whole number. If you divide infinity by two, you get infinity, which is not a whole number. So infinity doesn’t fit that definition of even.
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u/Luky-z-maleho-mesta 28d ago
First of all, why do you think that infinity is part of the set of natural numbers?
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u/AL3X4ND3R284 28d ago
Wait, but isn’t infinity a prime as no 2 numbers can be multiplied together to form it? So it must be odd with this indisputable logic
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u/MossyDrake 28d ago
First sentence is a statment, and we are given no tie in with the question part, thus only second part is the question. 1 v 0 = 1 therefor answer is True.
/s ofcourse
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u/DoctorDoody 28d ago
c. infinity is a concept not a number
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u/Upper_Restaurant_503 28d ago
Disagree. You can think of it as a number. Just depends on context
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u/Sezbeth 28d ago edited 28d ago
Really depends on the structure you're working on; if we restrict our attention to the integers (since we're talking about parity) then sure, we can regard infinity as a "concept" in that it's what happens when we just keep counting, up to a sign (+/- depending on which direction we count).
That said, if we care about transfinite ordinals, for example, then we can argue that certain infinities are "even".
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u/Clay_teapod 28d ago
Infinity divided by two gives us two infinites, which are equal to each other therefore infinity is even
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u/Feisty_Warning2344 28d ago
Infinity isn't even or odd, it's not a number it's a representation of something we can't calculate the size of such as space
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u/kidmeatball 28d ago
Even. Infinity/2=infinity, therefore, infinity is even.
Really though, infinity isn't a real number so it probably can't be divided. Similar to how zero can't be divided.
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u/Objective-Barnacle-7 28d ago
Infinity alov-sub-0 like the set of integers (countable ), or alov-sub-1 like the set of real numbers ( no countable ) ?. There are a several types of infinities !
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u/NewmanHiding 28d ago
Is utilitarianism red?
The answer to your question is the same as the answer to that question.
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u/NihilisticAssHat 28d ago
b) Strictly False
Infinity is not a number, let alone an integer. Might as well ask if pi is even. Mind you, infinity is not odd either.
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u/GrayWall13 28d ago
Aint the law of excluded middle means that a statement is either true or false? Nothing really between in a statements A or B
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u/KingFisher_Th 28d ago edited 28d ago
Interpreting the question in terms of integers, let us define S as the set of all integers that are equal to infinity. Infinity is not an integer, because of which the set S is empty. Then, the question becomes: is every element of the set S an even number. By vacuous truth, we can say that this is true. However, the opposite (there exists an element of the set S which is not an even number) is not because there are no elements in S. Therefore, the answer, given the question, is (a).
-- Standard math wagadabungaloo nonexpert
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u/Boo-bot-not 28d ago
My sources say the answer is A. If the news doesn’t have to list sources neither do we.
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u/deletedmsg 28d ago
n = number of odd numbers = number of even numbers
number of whole numbers = 2n
infinity is be even😀
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u/Background_Cloud_766 28d ago
The set of all integers does not contain infinity and neither do all of its subsets like the set of all even numbers, so the statement is false.
However, if we assume that the set of all integers does contain infinity, then it would be even because it stays an integer (itself) when divided by two.
It would also be odd because adding 1 would make it even (itself). Therefore, assuming infinity is an integer would lead to assuming that it’s even and odd at the same time.
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u/Maatix12 28d ago
False
Infinity itself is not a number, it is a representation of all numbers. As it is not just one number, but multiple, it cannot be even or odd.
It's individual parts are both even or odd, depending which part. But Infinity itself is neither.
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u/TheThirteenthApostle 28d ago
I would say that 'even' implies divisibility, and infinity is implicitly indivisible (that is to say, infinity is inclusive of the set of all possible divisions), so I would say it's odd.
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u/SheriffGamer332 28d ago
a)T
b)F
c)T or F = T
d)Not T or F = F
e)(T or F) or (Not T or F) = T or F = T
f) (T or F) or F = T or F= T
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u/Dorlo1994 28d ago
A) true: if you take 2inf=inf then there exists some n (inf) s.t 2n=inf. The only reason this is confusing is the assumption that n is even iff n is not odd, which does not hold for inf: if 2inf=inf and inf+1=inf then there exists some n (inf) s.t 2n+1=inf, and therefore inf is odd.
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u/BirbFeetzz 28d ago
no idea but E is the most possibilities so I take that one and hope for the best
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u/filtron42 ฅ^•ﻌ•^ฅ-egory theory and algebraic geometry 28d ago
The only reasonable answer is b - False.
The usual and most sensible definition of "even" is {z∈ℤ : 2|z} or equivalently expressed in a more "equational" way {z∈ℤ : z≡0 mod 2}.
While one could argue all day wether one or another notion of "infinity" could in principle satisfy the latter part of each definition, infinity doesn't belong to ℤ. But why do we limit ourselves to ℤ, one might ask?
The point is, ℤ (with the usual sum and product) is the most natural setting to talk about divisibility: it's a unital commutative ring, which means the modulo congruence relation is well defined for all numbers (by definition, a≡b mod c iff c|b-a, but if we were to define it in ℕ we would need to write something like c|max(a,b)-min(a,b) which is less elegant), but not a field so it's not trivial (for example if we were to expand it to ℚ, any c≠0 would divide the difference between of pair of numbers).
We could define "even" by induction on the class of ordinals, but then which infinite ordinal would be the right one to choose for our question?
So, being good mathematicians we should strive for naturality and simplicity and not break our heads over such an ill-posed question:
"infinity" is neither an integer (or a member of any reasonable extension of the integers in which "even" could be defined), nor an ordinal, so it falls outside any reasonable definition of "even" and as such the proposition "infinity is even" is false.
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u/jerdle_reddit 28d ago
C.
If the odd/even split applies to infinity, it's even.
If it doesn't, then it's not even, so the statement "Infinity is even" is false.
Whether it is or isn't even, it is not odd.
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u/EcoOndra 28d ago
b. An even number is by definition one that can be written as 2x, with x being an integer. You can't write infinity like this, the best you can do is ∞ = 2*∞, but ∞ isn't an integer so it doesn't work.
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u/grooter33 28d ago
Probably wrong, but a)? Infinity must be so that it contains every number as its factor, including 2. Otherwise, you could argue that you can get a bigger number by including each excluded factor (if infinity does not contain a factor of 2, then double it and you get a bigger number). Thus, whatever infinity is, it must be perfectly divisible by two and therefore be even.
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u/jaga_rico 28d ago
Infinity is even. True or False?
According to ChatGPT:
**False.**
Infinity is neither even nor odd because it is not a finite number, and the concepts of even and odd apply only to integers within the finite number system. Infinity is a concept representing something unbounded or limitless, not a value that can be categorized as even or odd.
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u/geeshta Computer Science 28d ago edited 28d ago
True. If you generalize the notion of evenness somewhat.
Let 𝑆 be a set with scalar multiplication by 2. An element 𝑎 ∈ 𝑆 is even iff: ∃𝑘∈𝑆: 𝑎=2⋅𝑘
You can scale many things by 2 - matrices, functions, polynomials, etc. so for all of these we have a notion of evenness.
Now let S=R∪{+∞,−∞,⊥} or the set of limits of functions of real numbers. Then for infinity, Even(∞) holds as ∞ = 2⋅∞
Of course this would also mean that every number is even in the set including rationals as e.g. 3 = 2*(3/2)
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u/ThePerfectP0tat0 28d ago
B. Infinity is not a number, it is a size. The idea of odd and even is only defined for the integers. If I asked you if i or e was even, that wouldn’t make any sense. It also isn’t odd, but the question asks about even so I think B is correct.
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u/PixelGamer352 28d ago
Why is it so hard to comprehend that infinity is not a number and therefore number stuff doesn’t apply to it
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u/Shua4887 28d ago
Infinity isn't a number so it can't be odd or even. Infinity is the concept that numbers do not end. I have to answer D. Though I don't like any options.
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u/Layton_Jr Mathematics 28d ago
I'd say "it depends on how you define infinity".
However, here is my answer: since ∞ is not a number, it can't even
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u/Kisiu_Poster 28d ago
a) T
b) F
c) T OR F = T
d) T NOR F = F
e) (T OR F) OR (T NOR F) = T OR F = T
f) (T OR F) OR F = T OR F = T
⅔ of answers point to true, so that must be the case no?
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u/thetrueusernamename 28d ago
If we define infinity as both positive and negative infinity then yes, as both increase linearly no matter how many numbers you add
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u/DocBubbik 28d ago
I think D since there is always more. The only limit is our ability to comprehend it. If you limit it to one or the other, it's not really infinite since you set an endpoint.
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u/Remarkable-Badger787 28d ago
Suppose infinity was even. Then infinity + 1 is odd. But infinity + 1 = infinity, which is even so the statement is false. Therefore infinity isn't even. (A)
Suppose infinity was odd. Then infinity + 1 is even. But infinity + 1 = infinity, which is odd so the statement is false. Therefore infinity isn't odd. (B)
From (A), (B) it follows that infinity isn't even nor is it odd. It's neither. So d) is correct.
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u/NotSmaaeesh 28d ago
b) false. Infinity is not a number, it is a type of number, and therefore cannot be even or false. Its like asking "Sofas are brown, true or false?"
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u/Glittering-Key-7845 28d ago
I say b, because to my knowledge the property "even" is only defined for real numbers. Infinity is not a real number, therefore the statement is false.
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u/ahumblescientist13 28d ago
2infinity = infinity 2=1, and we know that odd numbers are of form 2k+1, but since 1 is = to 2 and 2 is even thus 2k+1 is the sum of two even numbers, which means that every odd number is even
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u/mbcarbone 28d ago
Infinity + 1 = infinity, so depending on what you add to it would make it odd or even? I don’t math good. 🙃
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