Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [soft-question]

For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.

For questions whose answers cannot be objectively evaluated as correct or incorrect, but which are still relevant to mathematics.se.

12079 questions
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Why do we name equations more in applied math?

In pure math, equations aren't often named. For instance, we might define that $f$ is a (real) polynomial function iff there exists a finite sequence of real numbers $a_i$ such that $$f(x)=a_0 + a_1 x + \cdots a_n x^n.$$ Notice, though, that we…
goblin GONE
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The meaning of "The introduction of numbers as coordinates is an act of violence"

I found the quote The introduction of numbers as coordinates is an act of violence. from this answer from https://mathoverflow.net is very interesting. Unfortunately, I can not understand it. I asked for elaboration below that answer and have not…
Akira
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Interesting real-life examples of functions with multivariable range

The ones I can think of right now: Location of a person Temperature at every latitude and longitude (all looked at once) I can think of more examples but they are just - calculating one quantity for several things or at several places. What are…
user1752323
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Need help understanding mathematical statements

From https://en.m.wikipedia.org/wiki/Chinese_remainder_theorem Let $n_1, ..., n_k$ be integers greater than 1, which are often called moduli or divisors. Let us denote by $N$ the product of the $n_i$. The Chinese remainder theorem asserts that if…
Ashley
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How to define non-trivial necessary and sufficient conditions?

Mathematicians often speak of finding necessary and sufficient conditions for some property $P$. But $P$ is a necessary and sufficient condition for $P$. So, how do we determine what a non-trivial necessary and sufficient condition is? Is there a…
user107952
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What is the meaning of this number displayed in my R environment?

My question is really silly, I want to know what the meaning of this number displayed in my R environment, is it $2.2\times e^{-16}$?
user42912
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How do you approach doing research on an unsolved mathematics problem?

I have difficulty gathering all the information I need on open questions. How do I obtain all of the historical and technical details of a problem (e.g. a millennium problem)?
Paladin
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Coordinate geometry - its 'other way round'.

In coordinate geometry we solve the problems of geometry using techniques of algebra. What's the other way round? I mean to solve the problems of algebra (like proving the binomial theorem, etc.) using methods of geometry. Any suggestions please.
Awe Kumar Jha
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Zero function is often a solution?

I wonder why do we get zero as the trivial solution many a times. For instace: The ordinary differential equation $y'=y(y-1)$ has $y=0$ and $y=1$ as its trivial solutions. Zero is the trivial solution of the homogenous system of line eqations.…
Learning
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Killing inconsistencies: the path to understanding

This is a very soft question, and I ask it with some trepidation. When I begin studying a new topic, I don’t feel I really understand it until I go to bed Friday thinking I’ve found an inconsistency in mathematics, spend Saturday mulling over the…
Michael Weiss
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Can I read mathematics textbook like the music sheet?

During my Masters degree, I tried doing a proof with a pen and paper in my hand. This took me days to figure out. Today, I saw a proof and began to follow each step with a full comprehension of what was done without having to solve. This made me…
Omojola Micheal
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Structure of infinities and infinitesimals

It is probably obvious that my education in math is very small. However, it is one of the subjects I enjoy reading. So, if this is too far off the wall, I ask your forgiveness. I understand infinity as the name of a process. I see it as if…
user756686
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How Much Is Too Much When It comes to understanding from first principles?

My attempt to take math more seriously awoken a dormant obsession of trying to deconstruct everything to it's bare bones, and of not being satisfied with superficial understanding. As a rule of thumb i don't understand anything until i can prove it…
Simo
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How do I figure out what field a question or problem belongs to?

Are there guidelines somewhere? I have no significant background in math, but on my own I have come across some things that have really started to capture my imagination. I don't where to go from where I am now. *note: I added the soft-question tag…
Tricky
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$f(a)f(b)-f(c)f(d) = (f(a)-f(c))(f(b)-f(d))$

Is there an operator $f$ such that $$f(a)f(b)-f(c)f(d) = (f(a)-f(c))(f(b)-f(d))$$ $$f(a)f(b)+f(c)f(d) = (f(a)+f(c))(f(b)+f(d))$$ That would be interesting to see.
Martund
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