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6 votes
2 answers
296 views

Schwartz function test

An important class of functions in mathematical analysis, transform theory, and elsewhere is sometimes called Schwartz functions, after the French mathematician Laurent Schwartz. Informally, they are ...
David G. Stork's user avatar
0 votes
1 answer
89 views

Using the mathematical typography of formal logic

As asked in this question, I strongly prefer to use "mathematical" typography in Mathematica over text-based ("computer science") typography. Nevertheless, it sometimes fails for ...
David G. Stork's user avatar
3 votes
2 answers
183 views

Prove the second derivative of a function has a zero in an interval given constraints

I'm wondering how to express this question in a form computable by Mathematica: Assume $f(x), f^\prime (x),$ and $f^{\prime \prime} (x)$ exist and are continuous for all $x$. $|f(x) - \sin x| \leq 1/...
David G. Stork's user avatar
2 votes
2 answers
111 views

Pattern or ForAll statment in Assumptions

I would like to simplify an expression like $\sum _{i=1}^k \sqrt{a_i^2}$, with the condition $\forall _{i\in \mathbb{Z}_{>\, 0}}a_i\in \mathbb{R}_{>\, 0}$ and with $k$ being undefined, which ...
Mammouth's user avatar
  • 481
2 votes
1 answer
117 views

Input typography using quantifiers such as `ForAll`

Whenever possible I prefer to express inputs in mathematical notation (rather than text commands) as I feel this helps one think like a mathematician, leaving the calculations to Mathematica "in ...
David G. Stork's user avatar
5 votes
2 answers
162 views

Prove a relation involving Floor holds for arbitrary $n$

The 1968 International Mathematical Olympiad asks contestants to prove this relation involving the floor function for all $n \in \mathbb{N}$: $$\left\lfloor \frac{n + 2^0}{2^1} \right\rfloor + \left\...
David G. Stork's user avatar
2 votes
4 answers
169 views

For all x in {1,2,3}, x is bigger than 4

I am new to ForAll or Exists command. Resolve[ForAll[x, Element[x, Reals], x > 4]] gives ...
imida k's user avatar
  • 4,315