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 Feb5 comment continuity of the inverse function math.stackexchange.com/questions/143988/… Jan26 comment Geometric proof of complex number equation $e^{i\theta}$ lies in the unit circle, $|z-w|$ is the distance between $z$ and $w$, and $\sqrt{2}$ can be seen as the length of the diagonal of a square of side 1. Jan16 awarded Yearling Jan14 comment Extremely hard and stimulating (undergraduate) real analysis $problems$ Jan3 comment Deceptively simple divisibility problem @tmrlvi but there is no $k$ such that $9=2a+b\mid (a+b)^k=7^k$. Jan2 comment How can I prove these generalizations of Weierstrass? Glad it helped. Jan2 comment How can I prove these generalizations of Weierstrass? Okay. $\lim_{x\to +\infty}f=+\infty$ iff for every real number $M$ there is a real number $b$ such that $f(x)>M$ if $x>N$ (this is the definition). Now, taking $M=f(a)$, we find a real number $b$ ($>a$ because the domain of $f$ is $[a,+\infty)$) such that $f(x)>f(a)$ if $x>b$. By the extreme value theorem (Weierstrass' th.), there is a real number $c\in [a,b]$ such that $f(c)\le f(x)$ for all $x\in [a,b]$. In particular, $f(c)\le f(a)$ and $f(a)f(a)$ if $x>b$. Now you can find the minimum of $f$ in $[a,b]$. Dec20 comment elementary topology exercises reference See Elementary Topology: Problem textbook Dec20 awarded Constituent Dec16 answered Irreducible in $\Bbb Q[x]$ Dec15 awarded Custodian Dec15 reviewed No Action Needed Are there number systems corresponding to higher cardinalities than the real numbers? Dec10 comment The number of one-dimensional vector spaces in a field Dec10 comment If $\sum x^6_n$ converges, then $\sum x^7_n$ converges too Hint: In $[0,1]$, we have $x^7\le x^6$. Dec9 awarded Caucus Dec8 comment Prove or disprove: there is an integer $x$ so that $x \equiv 2$ (mod 6) and $x \equiv 3$ (mod 9). Glad it helped you, @GabrielH Dec8 answered Prove or disprove: there is an integer $x$ so that $x \equiv 2$ (mod 6) and $x \equiv 3$ (mod 9). Dec7 comment How to draw a quotient space @user42912 They're there to indicate the "positive direction", but don't pay attention to them. You're welcome.