1,705 reputation
419
bio website reddit.com/r/…
location meatspace
age
visits member for 2 years, 10 months
seen 2 hours ago

when someone smiles at me, all I see is an ape bearing its teethe


Jul
25
accepted How to prove that $\frac{10^{\frac{2}{3}}-1}{\sqrt{-3}}$ is an algebraic integer
Jul
25
comment How to prove that $\frac{10^{\frac{2}{3}}-1}{\sqrt{-3}}$ is an algebraic integer
I see that it does lie in said splitting field, but could you explain more what you mean by the rest of your comment?
Jul
25
revised How to prove that $\frac{10^{\frac{2}{3}}-1}{\sqrt{-3}}$ is an algebraic integer
added 82 characters in body
Jul
25
asked How to prove that $\frac{10^{\frac{2}{3}}-1}{\sqrt{-3}}$ is an algebraic integer
Jul
23
accepted My book states that $\sum_{n=1}^{\infty}r^{-n} = \frac{1}{r-1}$ for $r > 1$
Jul
22
accepted Strange application of Cauchy's Integral Theorem
Jul
22
comment Strange application of Cauchy's Integral Theorem
Ohhh I see it! Thank you for this.
Jul
22
asked Strange application of Cauchy's Integral Theorem
Jul
19
comment My book states that $\sum_{n=1}^{\infty}r^{-n} = \frac{1}{r-1}$ for $r > 1$
thankssssssssss
Jul
19
comment My book states that $\sum_{n=1}^{\infty}r^{-n} = \frac{1}{r-1}$ for $r > 1$
Ohhh gosh ok that clears things up, thanks.
Jul
19
asked My book states that $\sum_{n=1}^{\infty}r^{-n} = \frac{1}{r-1}$ for $r > 1$
Jul
17
comment Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$
Yes but in this case we are ok right?
Jul
16
answered Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$
Jul
16
comment Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$
Ok so past some point $x_0$ or within some neighborhood of a point, that makes sense; thanks! I think I'm going to spend some time proving those identities you listed to help my understanding.
Jul
16
comment Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$
So when we say $g=O(f)$ what we're saying is g is some element of the set of all functions whose absolute value is bounded by a constant multiple of $f$, is that a correct understanding?
Jul
16
comment Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$
why can't you then just set A to be the max of your bounded function?
Jul
16
comment Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$
Also, can I essentially just replace $O(f(x))$ with $Af(x)$ for $A$ some unknown positive constant?
Jul
16
comment Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$
Thank you Norbert. Could you explain your justification for getting rid of the log in the third equals sign?
Jul
16
asked Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$
Jul
16
comment Help Proving that $\frac{(1+\frac{1}{t})^t}{e} = 1 -\frac{1}{2t} + O(\frac{1}{t^2})$ for $t\geq 1$
@did: could you explain the missing step for me?