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23h
comment Assumptions in Word Problems (Calculus)
@Aakarsh For the same reason that if somebody gives me an ingredient list for chocolate pudding, I don't assume that they're forgetting to mention the two tablespoons of anchovy paste. It's not like the question is ambiguous, and the phrasing might imply there's a leak. There is absolutely no indication that there's a leak. That's something that you invented entirely.
1d
comment Mathematics - The big picture
This is sort of pretty but has close to zero informational value.
Aug
17
comment how to hinge-dissect an 1-omino to 3-omino?
There's no (dissections) tag?
Aug
16
comment Relaxed magic squares
You might be able to simplify the problem with a bit of group theory... note that relaxed magic square are preserved under row or column swap and rotations.
Aug
16
comment Is $a \circ b = \sqrt{a^2+b^2}$ ever a group?
@MichaelTMckeon Actually, considered purely with the operation $\circ$, $\mathbb H$ is indeed a commutative group.
Aug
16
comment Is $a \circ b = \sqrt{a^2+b^2}$ ever a group?
@MichaelTMckeon $\mathbb H$ isn't a ring.
Aug
16
comment Is $a \circ b = \sqrt{a^2+b^2}$ ever a group?
Is this the same as the algebraic closure of $\mathbb Z_2$?
Aug
16
comment Is $a \circ b = \sqrt{a^2+b^2}$ ever a group?
@StevenStadnicki Feel free to leave that example as either a comment, an answer, or even an edit to this answer.
Aug
16
comment Is $a \circ b = \sqrt{a^2+b^2}$ ever a group?
If $a,b\in \mathbb Z$ then the operation is not even closed, and are you sure there are inverses? The identity is clearly $0$, so what is the inverse of, say, $1$?
Aug
16
comment Is $a \circ b = \sqrt{a^2+b^2}$ ever a group?
Note that if we're going to be considering this over more general algebraic structures, you need to ask yourself what $\sqrt\cdot$ means.
Aug
15
comment Why isn't the volume of a sphere $ π^2r^3?$
@JoonasIlmavirta The OP is multiplying the area of the rotating disc by the distance it was rotated.
Aug
14
comment Is a set of some $m \times n$ matrices a relation?
While I see what you mean by "a matrix is two dimensional", that's a matter of how we think about them, it's not a precise mathematical quality, which makes the question hard if not impossible to answer.
Aug
14
comment Is a set of some $m \times n$ matrices a relation?
You don't "lose" anything just by changing your point of view, so I don't see the problem.
Aug
14
comment Factoring numbers
@DerekOrr Then $3$ probably isn't going to work. However, I don't have any ideas on figuring out what number could work.
Aug
13
comment How to model a real-world graphical structure into a mathematical formulation?
"Input = thoughts, output = equation. How?" There is no way. This does not happen. You cannot take vague thoughts and convert them into mathematical symbols, because that is not what mathematical symbols are for.
Aug
13
comment How to model a real-world graphical structure into a mathematical formulation?
I think you're overthinking things. What insights are you really going to gain from expressing a problem using a particular set of symbols convened on by a particular group of early 20th century intellectuals?
Aug
13
comment How do you express “a tree is composed of leaves, branches and roots” using mathematical symbols?
@LancePollard If you want to know how mathematicians think about problems, the answer is... absolutely not in the way you're apparantly trying to. If you can't tell at a glance how something can be represented mathematically or with set theory, that's probably because it's not worth trying to, and most importantly, representing a problem using symbols won't magically help you solve it.
Aug
13
comment Iterated Pi function
Searching the OEIS gets you this although there doesn't appear to be much information.
Aug
12
comment How do you express “a tree is composed of leaves, branches and roots” using mathematical symbols?
You wouldn't. That's not what mathematical symbols are for.
Aug
11
comment Logic behind dividing negative numbers
@JohnSmith Thinking of negative numbers as debts is as damaging as thinking of positive numbers as lengths.