What is infinity divided by infinity? - Mathematics Stack Exchange
2012年8月11日 · I know that $\\infty/\\infty$ is not generally defined. However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for
Proving De Morgan's Law with Natural Deduction
2015年2月26日 · Just a little uncomfortable with step 6 of part 2, i.e., using three steps (1,4,5) to assert a contradiction - seems like too much intuition for my liking.
Modulo 2 binary division (XOR not subtracting) method
I have attached an image showing a Modulo 2 binary division. I can roughly understand the working below which is using XOR calculation but I am not sure how the answer (in red) is being computed ...
Calculus proof for the area of a circle - Mathematics Stack Exchange
2012年8月28日 · I was looking for proofs using Calculus for the area of a circle and come across this one $$\int 2 \pi r \, dr = 2\pi \frac {r^2}{2} = \pi r^2$$ and it struck me as being particularly easy.
Good book for self study of a First Course in Real Analysis
2011年9月6日 · For self-study, I'm a big fan of Strichartz's book "The way of analysis". It's much less austere than most books, though some people think that it is a bit too discursive.
discrete mathematics - Show that (p ∧ q) → (p ∨ q) is a tautology ...
2016年3月7日 · I am having a little trouble understanding proofs without truth tables particularly when it comes to → Here is a problem I am confused with: Show that (p ∧ q) → (p ∨ q) is a tautology The firs...
Prove that $1^3 + 2^3 + ... + n^3 = (1+ 2 + ... + n)^2$
HINT: You want that last expression to turn out to be $\big(1+2+\ldots+k+(k+1)\big)^2$, so you want $(k+1)^3$ to be equal to the difference
What's the difference between theorem, lemma and corollary?
Terence Tao (Analysis I, p. 25, n. 4):From a logical point of view, there is no difference between a lemma, proposition, theorem, or corollary - they are all claims waiting to be proved.
Taylor series for sin (x) centered at pi - Mathematics Stack Exchange
2016年11月7日 · I haven't been able to figure this problem out. For the Taylor series I got: $$\sin{x}-0 = 0 - (x - \pi ) + 0+ \frac{1}{6} (x-\pi)^3 + 0 - \frac{1}{120} (x-\pi)^5 + o ...
complex analysis - Cauchy-Riemann equations in polar form ...
2015年4月22日 · Show that in polar coordinates, the Cauchy-Riemann equations take the form $\dfrac{\partial u}{\partial r} = \dfrac{1}r \dfrac{\partial v}{\partial \theta}$ and ...