# Tagged Questions

For requesting, clarifying, and comparing definitions of mathematical terms.

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### Nichtnegativstellensatz the same as Handelman's Theorem?

Wikipedia on "Handelman's theorem: If $K$ is a compact polytope in Euclidean $d$-space, defined by linear inequalities $g_i ≥ 0$, and if $f$ is a polynomial in $d$ variables that is positive on $K$, ...
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### Perfect powers by Oblath's result [duplicate]

What do you mean by this statement? Obl\'ath proved that the only perfect powers all of whose digits are equal to a fixed one $a \neq 1$ in decimal representation are 4, 8 and 9. This is equivalent ...
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### What is the square root of complex number i?

Square root of number -1 defined as i, then what is the square root of complex number i?, I would say it should be j as logic suggests but it's not defined in quaternion theory in that way, am I wrong?...
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### Is there a meaning to the notation “\arg \sup”?

When $f$ is a function on a set $A$, the notation: $\arg\max_{x\in A} f(x)$ denotes the set of elements of $A$ for which $f$ attains its maximum value. This set may be empty, for example, if $f(x)=x$ ...
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### Arithmetic-definability of geometrically-defined arithmetic concepts

Arithmetic-definability of geometrically-defined arithmetic concepts For purposes of discussion take arithmetic to be the study of the [ positive real] numbers, sequences of numbers, etc. and take ...
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### Formal definition of “counterexample”.

What is the preferred formal definition of “counterexample” as in: zero is a counterexample for "every integer is either positive or negative". Where in the literature is the notion of “counterexample”...
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### Is there a concept of “Cross determinant”?

Suppose $A = \begin{bmatrix}a & b \\ c & d \\\end{bmatrix}$. The determinant of $A$ is $$\det A = ad - bc.$$ Suppose $B = \begin{bmatrix}e & f \\ g & h \\\end{bmatrix}$. Now one could ...