#tropical geometry

[intrinsically-disordered-proxein]

how i learned about tropical geometry the hard way as an ecologist

[gay-mathematician-portmanteau]

single thread math episode 9: there's been a lot of talk on here about these taylor polynomial things, so i went to the equator to prove that they're nonsense.

claim: the maclaurin expansion for \e^x\ is not equal to the function \e^x.\ proof: consider the maclaurin expansion given by $$1+x+(1/2)x^2+…+(1/n!)x^n$$. this is trivially equivalent to $$1 \land x \land ((1/2)+2x) \land … \land (1/n!!)+nx$$. this can be rewritten as the piecewise function $$\begin{cases} 1&\text{if} x \le 0\\lim_{n \rightarrow \infty} \frac{1}{n!}+nx&\text{if} 0 < x \end{cases}$$ examine also $$e^x = \prod_{1}^{x}(e) = \sum_{1}^{x}e = ex$$.

it is easy to see that these functions are not equal to one another.

i don't know why anyone studies anything other than algebra. you're welcome, analysts.

[backward-indication]

today’s USA today crossword had clue:

genus of tropical trees

sadly, the answer was not zero

[isomorphismes]

The tropical semiring is arithmetic piped through a log with base →∞.

Also if you or someone you know  is first encountering a squeeze theorem or other a≤x≤A type reasoning, remark 2.1 might be a relatively painless calisthenic to warm you/them up to a≤x≤A type arguments.

by Gregory Mikhalkin