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Given
$$T_m(x,y)=\min(x,y),$$
for all $x,y\in[0,1]$.
Prove if $y\leq z$ then $T_m(x,y)\leq T_m(x,z)$, for all $x,y,z\in[0,1]$.
Given,
\begin{align*}
T_m(x,y)&=\min(x,y).
\end{align*}
For first cases $x\leq y$,
\begin{align*}
T_m(x,y)&=x.
\end{align*}
Give...
In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. A t-norm generalizes intersection in a lattice and conjunction in logic. The name triangular norm refers to the fact that in the framework of probabilistic metric spaces t-norms are used to generalize triangle inequality of ordinary metric spaces.
== Definition ==
A t-norm is a function T: [0, 1] × [0, 1] → [0, 1] which satisfies the following properties:
Commutativity: T(a, b) = T(b...
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There was recently a question about a flux through a surface. The idea is to use the formula:
$$\iint_S \mathbf F \cdot d\mathbf S,$$
with $\mathbf{F} = x \boldsymbol{\hat{\imath}}+ y \boldsymbol{\hat{\jmath}} - 2z \boldsymbol{\hat k}$ and $S$ is the semisphere with radius $a$ and $z≥0$.
Si...
Proposal: Eliminate the tag transformation.
The tag transformation is too broad—there are a large number of things in mathematics called "transformations" coming from diverse parts of mathematics, and tagging a question with this tag does nothing to refine or sort these different notions. I...
