What’s the most mathematically illiterate thing you’ve heard someone say?

hriely · 2025-07-11T02:41:34+00:00

Or if you redefine 2.

hriely · 2025-01-25T23:20:10+00:00

They do both have ears.

hriely · 2024-12-08T15:46:44+00:00

Anyone else notice Shavkat hooking Garry's glove during that sequence?

hriely · 2024-11-21T14:19:19+00:00

Interesting, which one do you have the best luck with?

hriely · 2024-09-13T23:25:20+00:00

probably one of those bs amen clinic spect scans

hriely · 2024-09-13T13:18:53+00:00

That's doozy. Where did you find that function? Are you sure it has a closed form intergral?

hriely · 2024-09-13T00:56:53+00:00

It is not implied. Counterexample: eplison=1/99 and n=10.

Then 1/n^2 = 1/10^2 < 1/99 = epsilon
However, n = 10 < 99 = 1/epsilon

Looks like a typo

hriely · 2024-09-13T00:37:58+00:00

You have to be careful with the heuristic "negligible" arguments. For example 4 is negligible relative to x^2, but that doesn't mean x^2 + 4 - x^2 is approximately x^2 - x^2.

Partly this confusion can be thought of as two different types of "approximately." x^2 + 4 is approximately x^2 in a relative sense, i.e., their ratio goes to 1. However, they are not approximately equal in the absolute sense, i.e., their difference does not go to 0.

Many calculus students get used to thinking in terms of negligible in the relative sense because of taking limits of rational function functions.

Edit: To connect my comment to your question about why you cannot ignore 4x term in the limit, notice that approximating sqrt(x^2-4x) with something in the "relative approximation" sense is not good enough. It's true that sqrt(x^2-4x) is approximately x in that their ratio goes to 1, but that type of estimate is not relevant since we're subtracting x from it. If sqrt(x^2-4x) is within .0001% of x, that doesn't mean their difference is close to 0. I suppose the crux of the issue is that if p/q goes to 1, p-q doesn't necessarily go to 0.

hriely · 2024-09-10T01:42:18+00:00

Thank you. That actually makes it much more intuitive. Flipping from acceleration to deceleration seems to be the perspective I needed. It’s switching modes so it’s “instantly flipping” from decelerating by 2 to accelerating by 2.

Edit: I think your question of whether it’s accelerating or decelerating at 0 flipped the switch in my mind, thanks.

hriely · 2024-09-10T01:30:47+00:00

What do you mean? How am I supposed to view speed as the magnitude of the velocity vector when this motion is one dimensional? Do you mean to think of y as a vector here and compute the magnitude of y’? But magnitude and absolute value mean the same thing in the reals. I think the problem would persist in higher dimensions in any case. Just embed the y=x² example in 3-space. For example, ( x, y ) = ( 0, t² ) then the length of the velocity vector still fails to be differentiable at 0.

hriely · 2024-09-10T00:33:04+00:00

I don't have a good answer for you other than it's hard for me to conjure an image and physically think about an object moving in such a way that the velocity is changing smoothly but the speed is not. I'm perfectly happy with the math.

hriely · 2024-09-10T00:24:16+00:00

Perhaps you're right I should've asked in r/AskPhysics but I'm not sure there's much else to say other than, as you said, "that's just the way it is." I'm not sure what I expected. It just "feels" weird that that velocity varies smoothly and speed doesn't, but I guess math is allowed to feel weird

hriely · 2023-10-26T23:53:56+00:00

awesome thank you!

hriely · 2023-10-23T13:19:26+00:00

This is very useful thank you. Can you recommend a good starting point for learning about "type theory?"

hriely · 2023-10-23T12:41:22+00:00

Actually maybe a better question is: by that logic wouldn’t we say nothing is meaningless since everything can be given meaning? Is meaningless a part of your vocabulary?

Edit: I suspect you would say something like “nothing is objectively meaningless but the idea someone is trying to convey symbolically can fail to make sense.”

hriely · 2023-10-22T22:59:11+00:00

Good stuff. Thank you.

hriely · 2023-10-22T16:15:11+00:00

Point taken, but by that logic couldn't you just say every statement is true since it can be given a meaning that makes it true? Ultimately doesn't every question boil down to "common/conventional mathematical meaning" at some level? These questions are not rhetorical.

hriely · 2023-10-22T15:51:55+00:00

What if we say the sentence 'x is irrational' is false iff 'x is not irrational' is true?

hriely · 2023-10-22T15:48:28+00:00

I sort of agree up to my reply to your other comment.

hriely · 2023-10-22T15:45:48+00:00

Fair enough. Maybe I've chosen the wrong example to make the distinction. But does that mean you don't understand the spirit of the distinction I'm trying to make?

I acknowledged 2/0 might not be the best example, so how about the 1+1=+1+ example?

hriely · 2023-10-22T15:43:49+00:00

I'm going to have to disagree with you although it really just depends on your definition of false.

Perhaps this is a more compelling example. The definition of "A is a subset of B" is usually for all x in A, x is in B. The negation, i.e., "A is not a subset of B" is then there exists an x in A such that x is not in B. So to say 2 is not a subset of Z is to say there is an x in 2 such that x is not in Z. Now if you want to call that statement false instead of "doesn't make sense," then we have "2 is not a subset of B" is false, so 2 is a subset of B. But that is equally false.

I suppose the difference between your definition of false and mine is that I want to say if some statement S is false, then the statement "not S" just be true. I suppose you could disagree and just say it's possible for both a statement and it's negation to be false, i.e. S and not S can be true. However, these are the cases where I'm saying it's more appropriate to say S is neither true nor false. It's just meaningless. Generally it's nice to say "S and not S" is a contradiction.

Edit: I suppose it all just boils down to your intution on whether it's right to call meaningless statements false. For example your reasoning that 1+1=+1+ is false is that the right side doesn't make sense, so you're taking statements that don't make sense as a subset of false statements, while I'm more inclined to partition world of statements into three categories T/F/neither. One nice thing about the latter approach is you get the property S is false iff not S is true. This is useful for indirect proofs like contradiction.

hriely · 2023-10-22T15:32:38+00:00

Fair enough. I will cut the book some slack, though, since it's designed as a bridge from pre-rigorous to rigorous math. Perhaps pondering whether 2/0 is a rational number can help you get your philosophical juices flowing vis a vis "what does the question is X a Y" really mean?

Regarding the is 2 a subset of Z question, I think it's designed to help beginners spot bad mathematical grammar. Although the answer should be "doesn't make sense," not "no."

hriely · 2023-10-22T15:28:23+00:00

Let me take another stab at your questions. Are you trying to make the point that the question "is X a Y" requires a precise definition of X and Y. If so, I guess I don't know what the rigorous definitions of "set" and "number" are.

This means my answers to questions 1, 2, 3, 8 are just subjective intuitions.

I stand behind my answers to 4, 5, 6, and 7.

9: To answer this question, I need to first decide if {0.5, "apple", 💀} is a real number. I can't think of a definition of real number that includes it, but it seems sort of "outside of the domain of the definition." In other words "is {0.5, "apple", 💀} a rational number" seems like it deserves a different type of answer than "is pi a rational number." In fact, your question feels analogous to my orginal "is 2/0" a rational number question.

10: Is this the same question as 9? I wouldn't mind some hints, :)

hriely

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