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2d
comment Terminology: Difference between Lemma, Theorem, Definition, Hypothesis, Postulate and a Proposition
A definition is just a 'naming' of an object and not like a theorem at all... a proposition is a theorem... usually an 'easy theorem' setting out some basic facts.
2d
answered How to show that $\varphi(x, y) = (f(x) + y^2, y^3)$ is injective?
Apr
22
revised If $a_n = \frac{e^{n}}{e^{2n}-1}$ how do I show that $a_{n+1} \leq a_n$?
added 324 characters in body
Apr
22
comment If $a_n = \frac{e^{n}}{e^{2n}-1}$ how do I show that $a_{n+1} \leq a_n$?
+1 for the another way... I don't fancy $\sinh n$ to be honest as showing that that is increasing needs (a little) work.
Apr
22
answered If $a_n = \frac{e^{n}}{e^{2n}-1}$ how do I show that $a_{n+1} \leq a_n$?
Apr
21
comment Why would I want to multiply two polynomials?
"That's what she said".
Apr
21
comment Root Calculation by Hand
...but are not these numbers coming from answers like the others?!
Apr
21
comment Prove every bounded sequence in the real numbers has a convergent subsequence using cauchy
en.wikipedia.org/wiki/Bolzano%E2%80%93Weierstrass_theorem : use peaks... this too: en.wikipedia.org/wiki/Monotone_convergence_theorem
Apr
21
comment unsure how to rearrange $f(x)$ into suitable $p(x)/q(x)$
I don't understand the point of the exercise you were doing to be quite honest with you.
Apr
21
comment unsure how to rearrange $f(x)$ into suitable $p(x)/q(x)$
...or else, do what you have with $\displaystyle f(x)=\frac{1+2/x^2-3/x^3}{1/x+3/x^2+4/x^3}=\frac{P(x)}{Q(x)}$... now $P(x)\rightarrow 1$ and $Q(x)\rightarrow 0$.
Apr
21
comment unsure how to rearrange $f(x)$ into suitable $p(x)/q(x)$
...do you not get it... the 'limit' is infinite... the question can't be done in the terms you are asking. The two answers here tell you what to do in this case... $f(x)\sim x$ so as $x$ gets big $f(x)$ gets big too.
Apr
21
comment unsure how to rearrange $f(x)$ into suitable $p(x)/q(x)$
@DanielCongedi As $x\rightarrow \infty$, considered "separately", ALL non-constant polynomials tend not to a finite value, but $\pm\infty$.
Apr
21
comment unsure how to rearrange $f(x)$ into suitable $p(x)/q(x)$
Yes the numerator tends to infinity. Well as $x$ goes to infinity, $f(x)$ begins to look like $x$ (in the sense that the percentage difference between them goes to zero), and if $x$ goes to infinity so does $x$... 30% at $x=10$, 3% at $x=100$ and 0.3% at $x=1000$: wolframalpha.com/input/…
Apr
21
revised unsure how to rearrange $f(x)$ into suitable $p(x)/q(x)$
deleted 11 characters in body
Apr
21
comment A simultaneous equation question
+1 for alternate solution
Apr
21
answered unsure how to rearrange $f(x)$ into suitable $p(x)/q(x)$
Apr
21
comment Connection between Functional Analysis and Quantum Physics
What are observable represented by? Under this axiom, what is the relationship between the observables and measured values of the observable? This stuff, which you must know, is functional analysis as @Omnomnomnom says... I think the best you can do here is as per your reference request tag.
Apr
21
comment Connection between Functional Analysis and Quantum Physics
This short question requires a very long answer. Do you know any quantum mechanics? Your starting point is an axiomatic treatment of quantum mechanics.
Apr
20
comment Is the sequence generated by two permutations periodic?
...how is the second sequence defined??? It seems ambiguous to me.
Apr
20
comment Are basic trigonometry functions ( sine, cosine, tangent ) intuitive or memorized?
+1 for "The base concept of trigonometry is similarity."