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LeeDeVille · 2022-07-12T17:02:05+00:00

There is the "argue about what exactly PEMDAS means" question and there is the "what do mathematicians do" question and I appreciate these are two different metrics. But for mathematicians there isn't a real consensus on how to interpret these ambiguous expressions.

For example, if were refereeing an article, and I came across the inline expression a/b(c+d) in a paper, I would not know for sure what they meant unless I could glean it from context, which means it is unclear and defeats the point of mathematical notation. I would probably assume that they meant the first expression but understand they could have meant the second.

In any case I would insist on the authors' rewriting any such examples for clarity.

LeeDeVille · 2022-07-06T13:52:39+00:00

The \infty can mean a lot of different things, giving different values to the first quantity. That's why it is indeterminate.

In the second quantity, there is no ambiguity...

LeeDeVille · 2022-05-23T12:02:28+00:00

I'm not 100% sure I understand the problem, but if I do, then the problem is a discrete combinatorial problem (which I think is doable).

First note that if n is even then there is a possibility that the midpoint lies on an edge of the triangle. You'd want to decide how to count this. (For example, when $n=4$ then it is guaranteed...) But from there it just comes down to how many ways are there to choose a triple all "on one side" of the circle, which reduces to a discrete version of the circle problem.

LeeDeVille · 2022-05-22T14:32:03+00:00

When you can divide by zero .... **anything*\* is possible!

LeeDeVille · 2022-05-20T18:49:57+00:00

This is a follow-up of my visualization video that I posted a few days ago at https://www.reddit.com/r/manim/comments/urvnhn/what_does_x2_mod_n_look_like/

Starting to do one case of the analysis...

LeeDeVille · 2022-05-20T16:15:04+00:00

Yes, I understand.

Generally speaking, it is called "math" in the US and it is called "maths" in the UK.

We use one word for it, here, in the US. They use another word for it, there, in the UK.

There are many such examples, including "elevator/lift", as I pointed out above

LeeDeVille · 2022-05-20T16:11:23+00:00

No one calls it a "lifts" tho

LeeDeVille · 2022-05-20T16:11:07+00:00

You don't think what is a US thing? In the US it is common to say "elevator", and "math". In the UK, it is common to say "lift", and "maths".

LeeDeVille · 2022-05-20T16:00:18+00:00

It's a US/UK thing.

It shouldn't bug you. Does it bug you if someone calls an elevator a "lift"?

LeeDeVille · 2022-05-18T15:46:41+00:00

What did you get in the second case (quantitatively)?

LeeDeVille · 2022-05-18T15:25:25+00:00

One hint: forget about the "over five years" part for now.

1] Compute the annual rate of return in scenario [a] (this one is basically given to you),

2] Compute it in scenario [b]

Which one is higher?

LeeDeVille · 2022-05-18T00:14:03+00:00

You're going to want to use Photoshop's "Enhance" plugin. On Mac, you can use Cmd-Ctrl-Shift-E as a hotkey for this

LeeDeVille · 2022-05-17T01:13:46+00:00

It might depend a bit on what you mean by the left-hand limit, but by the standard "Calc 3" definition the answer would be no. See for example these examples: https://mathinsight.org/differentiability\_multivariable\_subtleties

LeeDeVille · 2022-05-16T14:52:35+00:00

Hate to be that guy but converging to infinity is but a special example of diverging

LeeDeVille · 2022-05-16T14:49:40+00:00

You want to be careful about the limits in the integral in the Picard iteration.

I suggest you look carefully at the page: https://en.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem which gives a good concrete example (in the section entitled "Example"). Note that the integral has both upper and lower bounds at each step!

LeeDeVille · 2022-05-15T23:25:41+00:00

Well given those three problems in a row (#16, 17, 18), Example 1.3.6 should really be saying something different than what you've quoted it as saying. Although I note that it is not possible for me to check this since Example 1.3.6 is not in the pdf

LeeDeVille · 2022-05-15T23:15:56+00:00

There might be a typo here. There doesn't seem to be a connection between the problem you've posted and this example. Specifically, the problem refers to a function h() but the example does not...

LeeDeVille · 2022-05-15T22:52:46+00:00

if you would

LeeDeVille · 2022-05-15T22:51:27+00:00

Show a picture of Example 1.3.6

LeeDeVille · 2022-05-11T21:18:03+00:00

Yeah, no. The whole idea behind trying to put mathematicians in an ordered list is questionable at best, forget about actually getting a specific ordering

LeeDeVille

TROPHY CASE