View source for Trivial

==Meaning==
Trivial means "obvious", if something is trivial it means very little work needs to be done to show it holds. Trivial can also mean the argument is [[vacuous]], for example {{M|\forall x\in X[P(X)]}} holds, when {{M|X\eq\emptyset}} is it ''vacuously true''.
{{Disambiguation}}
* '''Algebraic objects:'''
** [[Trivial (group)]] - the group: {{M|(\{e\},*:\{e\}\times\{e\}\rightarrow\{e\})}} is called the [[trivial group]], {{M|e}} is the identity element and {{M|e*e\eq e}} is the only operation
** [[Trivial (ring)]] 
** [[Trivial (module)]]
** [[Trivial (vector space)]]
* '''Spaces:'''
** [[Trivial (ring of sets)]]
** [[Trivial (sigma-ring of sets)]]
** [[Trivial (topology)]] - {{AKA}}: [[indiscrete topology]]
*** {{Caveat|The [[trivial metric]] induces basically the exact opposite topology}}, the trivial metric, {{M|d:(x,y)\mapsto\left\{\begin{array}{lr}0 & \text{if }x\eq y\\ 1&\text{otherwise}\end{array}\right.}}, [[topology induced by a metric|induces]] the [[discrete topology]] - [[the power-set]] topology.
** [[Trivial (metric)]] 
{{Definition|Abstract Algebra|Group Theory|Ring Theory|Module Theory|Linear Algebra|Measure Theory|Topology|Metric Space}}