I’m taking my first course in real analysis, and I’m trying to prove the following proposition.
Proposition:
If $f:S\to\mathbb{R}$ is uniformly continuous, then $f$ is continuous.
In comparing seemingly similar definitions of continuity and uniform continuity, I noticed that the only difference i...
Would it be justified to synonymize first-order-logic and predicate-logic (both ~100 questions)? first-order-logic as the primary tag seems sensible to me.
The equation $x^5 - 2x^4 - 1 = 0$ has five complex roots $a, b, c, d, e$ . Find the value of $\frac{1}{a^8} + \frac{1}{b^8} + \frac{1}{c^8} + \frac{1}{d^8} + \frac{1}{e^8}$ .
I know so far Newton's identity can be used to find power sum of roots if the power is non negative but no idea what to ...
Find all real roots of the irrational equation $\sqrt{3x^2+x-1} + \sqrt{x^2-2x-3} = \sqrt{3x^2+3x+5} + \sqrt{x^2+3}$ .
My try :
Given, $\sqrt{3x^2+x-1} + \sqrt{x^2-2x-3} = \sqrt{3x^2+3x+5} + \sqrt{x^2+3}$ .
Let $u = x^2-2x-3, v = 3x^2+3x+5, w = x^2 + 3$ . Then, $3x^2+x-1 = u + v - w$ .
So, the ...
I need to prove the following
The variation $|\mu|$ of a complex measure $\mu$ is finitely additive.
The following is my attempt. Basically, my idea is to prove that $|\mu|(B_1\bigcup B_2)=|\mu|(B_1)+|\mu|(B_2)$ holds for any disjoint $\mathscr{A}$-measurable sets $B_1$ and $B_2$. I would reall...
Resolved. All occurrences of the tag have been removed.
I suggest to remove theory-of-equations tag.
This tag was created in December. The tag creator also provided the tag-excerpt and the tag-wiki which more-or-less follow the Wikipedia article Theory of equations. Looking at the tag-info,...
