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Currently at university studying maths.

Here is my github: https://github.com/cameron-martin


May
30
comment Polynomials vs polynomial functions
And the elements of $R[X]$ are in no way functions, so we can't write $f(x)$ for $f \in R[X]$?
May
30
comment Polynomials vs polynomial functions
@GitGud So a polynomial function is determined by the values it takes when evaluated in the domain of the function, whereas a polynomial is determined by it's coefficients?
May
23
comment What does d f(t,x) = 0 mean?
@ChristianBlatter What would be a less condensed way of writing this? I'm interested to know where the notation comes from.
May
23
comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)
@Cruncher which is zero. $\lim_{n \to \infty} 10^{-n} = 0$, as does $\lim_{n \to \infty} 10^{-n} b$, which corresponds to any $0.000...b_0...b_n$, where $b_k$ is the kth digit of the decimal expansion of b.
May
22
comment Definition of homogeneous ODE
I wish they'd explain this to us, some of our lectures notes are really quite sloppy in areas, mostly with the more applied modules. Thanks anyway :)
May
22
comment Definition of homogeneous ODE
Oh yeah, made an error in the question. Fixed it now.
May
1
comment How do I prove a basic and obvious-looking set relations?
Wouldn't we have to prove it from some axioms of propositional logic?
May
1
comment How do I prove a basic and obvious-looking set relations?
Doesn't this just reduce proving $A=A \cap A$ to proving $a \land a \Leftrightarrow a$? How would you go about proving the latter?
May
1
comment Vector space C over R's basis is linearly independent
So should I just work with ordered pairs all the way through, instead of using $a + bi$
May
1
comment Vector space C over R's basis is linearly independent
As an ordered pair. And $(a, b) = (0, 0) \Rightarrow a=0 \land b=0$
Apr
21
comment Expression as argument in function definition
Do you mean $x=c + d \sqrt D$ instead of $x=c + \sqrt d$, or am I mistaken?
Apr
21
comment Expression as argument in function definition
Surely you can choose $D$ to be anything you want though? Why does $D$ have to be the same as $d$? And is the $d$ you're using in your answer the same $d$ as in the question?
Apr
17
comment Alternative ways to say “if and only if”?
@AlexB. I don't follow why that is circular. Surely you want to say both: "If a group G is called simple, then these conditions hold." and "If these conditions hold, then group G is simple."
Mar
12
comment Proving that an infinite set is uncountable.
For a set S to be countable there must exist an injection from N -> S, where N is the set of natural numbers.
Mar
11
comment Two different coins on a chessboard
Remember to mark the question as the accepted answer if you think it is worthy.
Mar
11
comment Are there any other functions that behave the same as $ce^x$ with respect to differentiation
What do you mean by the constants will be different? Wouldn't you get the function $ce^x$, but defined on the domain $(-\infty, 0) \cup (0, \infty)$ when you differentiate it?
Mar
11
comment Are there any other functions that behave the same as $ce^x$ with respect to differentiation
@N.S. Can you elaborate on this?
Mar
11
comment Two different coins on a chessboard
Does this answer your question?
Mar
11
comment Two different coins on a chessboard
Updated my answer
Mar
11
comment Primitives in unique factorisation domains
What is $Z_2[X]$?