Recent content by mcastillo356

Lemma 2 is difficult to me Why ##A=A_{0}\sim{B_{1}}\sim{A_{2}}\sim{B_{3}}\sim{A_{4}}\sim{\cdots}##? Attempt ##A=A_{0}##, ##B_{1}=f(A_{0})##, and so on. Why is this a consequence of injectivity? Attempt A set mapping is injective if...

Working hard on it.

"The sting", that's my favorite movie. The soundtrack is amazing.

##\mathbb{R}^+##?

No idea. I can only attempt at it: ##F## could be the identity function? @martinbn says so. Another doubt: The Axiom of Choice is needed?

I'm working on the Schroether-Bernstein theorem, this is, the next step in the textbook "Introduction to topology and modern analysis", by Simmons. We assume that ##f:\,X\rightarrow{Y}## is a one-to-one mapping of ##X## into ##Y##, and that ##g:\,Y\rightarrow{X}## is a one-to-one mapping of...

Yes. Simmons is being precise. Into means inyective. That's accurate, indeed. Thanks, @fresh_42 !

The textbook is being fine. I asked the forum for some introduction to topology, and decided to start with Simmon`s. This naive question is due to ignorance of the words into and onto, which I don't distinguish in Spanish. A quick browsing sugests I'm right.

In fact, the cartesian coordinates are continous, and sine function too; this means the value of the limit at any points ##(x,\,y)## will be the same as the function's value. In this case: $$\displaystyle\lim_{(x,\,y)\rightarrow{(a,\,b)}}{f(x,\,y)g(x,\,y)}=LM$$ ##L## and ##M## being the values...

It is going to be hard work for me, but the link is very revealing. Simmons' "Introduction to topology and modern analysis" is the textbook I was looking for. Thank you, @mathwonk

My background is calculus, but I feel that, in calculus (my textbook is Calculus, by Robert Adams), I study limits, continuity, differentiation, integrals, etc, but, I realize that if we want cool things to happen in calculus, we need some basic topological concepts: I've taken a look at metric...

Now I understand the work of those who think and work about the essence of physics. Thank you, @fresh_42

I still don`t understand: which is the philosophy behind Newton`s second law of motion ##\vec{F}=m\vec{a}##, for example?. I can´t even provide any attempt. Yes, I can google it, but I find nothing new: mathematical empiricism, absolute space and time, forces as the cause of motion, etc.

I don't understand what is the difference between a physician and a philosopher on physics.

"The hell of the living is not something that will be. If there is one, it is what is already here, the hell we live in every day, that we make by being together. There are two ways to scape suffering it. The first is easy for many: accept the hell, and become such a part of it that you can no...