Stephen Nand-Lal
  • Member for 8 years, 8 months
  • Last seen more than a month ago
  • Liverpool, UK
What is the difference between "immersion" and "embedding"?
15 votes

Understandably there are a lot of answers, but if you still have any further questions maybe this will help. An embedding of a topological space $X$ into a topological space $Y$ is a continuous map $...

View answer
homeomorphism of cantor set extends to the plane?
8 votes

In $\mathbb{R}^2$, Schonflies theorem ensures that any two embeddings of Cantor sets are equivalently embedded, or equivalently that any homeomorphism $h$ between the two Cantor sets (it can be proven ...

View answer
Prove that $ \frac {12^{x-2}.4^{x}} {6^{x-2}} = 2^{3x-2} $
4 votes

$\frac{4^{2x-2}}{2^{x-2}} = \frac{(2^2)^{2x-2}}{2^{x-2}} = 2^{(4x-4)-(x-2)} = 2^{3x-2}$

View answer
The proportionality symbol
Accepted answer
3 votes

Either would be a valid equation but you'd get different values of C; I.e. if you take C to be the value that satisfies: $a=Cb$ Then we could also write this as: $aC^{-1}=b$ So you can view it ...

View answer
Finding math research problems
2 votes

I think that part of this question answers itself when you get "into" a field. When I was writing my MSc. dissertation I really had no idea what I was interested in, but my supervisor pointed me in a ...

View answer
What kind of mathematical operation is used to repeatedly increase a number by a certain percentage?
Accepted answer
2 votes

Its like compound interest! The general formula would be $10 \times 1.25^n$ where n is the amount of times you are "compounding the interest".

View answer
Can anyone help me understand the simplification of $\frac{\sqrt 3 + \sqrt 2}{\sqrt 3 - \sqrt 2}\;$?
2 votes

So if you consider:: $$\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} \times \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}} = \frac{(\sqrt{3} + \sqrt{2})^2}{(\sqrt{3} + \sqrt{2})(\sqrt{3} - \sqrt{2})...

View answer
On the pH scale, each unit change in pH represents a tenfold increase in acidity or alkalinity.
1 votes

Simply put isn't it 10^(3.8) ?

View answer
How come Cantor set is 'the' Cantor Set?
0 votes

In $\mathbb{R}^2$, for any two Cantor sets $A$ and $B$ we can find a homeomorphism $h \colon \mathbb{R}^2 \to \mathbb{R}^2$ which carries $h(A)$ onto $B$. This essentially says they're equivalently ...

View answer
Given the sample triangle below and the conditions, find the hypotenuse of the triangle
0 votes

We initially use the tan function: $\tan \left( \frac{5}{3} \right) = \frac{b}{a} = \frac{b}{16}$, so $b = 16 \tan(\frac{5}{3})$. You can then directly apply Pythagoras' Theorem, so: $c^2 = 16^2 + (...

View answer
Find the derivative of $\frac{{(x^3)^{4/3}}}{(2-x)^{4/3}}$
0 votes

This may be a different approach but you could consider your formula as: $f(x) =\frac{(x^3)^{\frac{4}{3}}} {(2-x)^{\frac{4}{3}}} = (x^3)^{\frac{4}{3}} (2-x)^{-\frac{4}{3}} = x^4 (2-x)^{-\frac{4}{3}}$ ...

View answer
Studying mathematics: Is proving things yourself worth the time?
0 votes

I'd say it very much depends on the context; if its a field you are comfortable in and you have a good grasp of the basic concepts then it definitely is. If, however on the other hand, you're ...

View answer
A question about manifolds with boundaries.
0 votes

Any point on the boundary will have a neighbourhood homeomorphic to a neighbourhood in $\mathbb{R}^2_+$; think of this pictorally - its neighbourhood will be a collection of interior points of the ...

View answer
imaginary number evaluation
0 votes

Youre meant to be evaluating the modulus of your answer, so $|\frac{3i+1}{5}| = \sqrt{\frac{9}{25}+\frac{1}{25}} = \sqrt{\frac{10}{25}} = \frac{\sqrt{10}}{5} = \frac{\sqrt{2}}{\sqrt{5}} = B$

View answer
Finding the tangent line to the graph of $f(x)=(x+2)^{3/5}$ at $x=-2$
0 votes

Try evaluating the gradient at points very close to $x = -2$, and see what happens as you approach $x$, to get some hints!

View answer
Creating a Topological group from modulo multiplication Group.
0 votes

Maybe a totally different approach would be to consider your elements as rotations of $\frac{2 \pi}{3}$ acting on a regular 3-gon i.e. an equilateral triangle?

View answer