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Background
Let $f: [0, \infty) \times {\mathbb R}^n \rightarrow {\mathbb R}^n$ be a jointly measurable function satisfying,
$f(t, \cdot)$ is locally Lipschitz for every $t \geqslant 0$,
for every compact $K \subseteq {\mathbb R}^n$ and every $b > a \geqslant 0$, $$
\int_a^b \|f(t,\cdot)\|_K\,dt <
So while trying to find the gradient of the surface given by the equation
x+y=5
The gradient was <1,1,0>
And then I multiplied both sides of the equation by negative 1 giving me
-x-y=-5
The gradient became <-1,-1,0>
So the gradient changed although it is the equation of the same surface... ...
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space. Intuitively, homotopy groups record information about the basic shape, or holes, of a topological space.
To define the n-th homotopy group, the base-point-preserving maps from an n-dimensional sphere (with base point) into a given space (with base point) are collected into equivalence classes, called homotopy classes. Two mappings are homotopic if one can be continuously deformed into the...
Moved from Math Overflow due to not being regarded as a high degree of research
Note: I am looking in particular at real valued/real input functions at all values regardless of differentiability.
In this question a series of axioms or postulates governing calculus are proposed. Granted, that is...
Rayo's function defined in English:
"$\operatorname{Rayo}(n)$ is the smallest positive integer bigger than any finite positive integer named by an expression in the language of first order set theory with $n$ symbols or less."
More formally, we make use of the following second-order formula (Sa...
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