/sci/ - Science & Math

>>15040990
If [math]X=Y[/math] then [math]X^Y=Y^X[/math] is trivially true.
Conversely, assume [math]X^Y=Y^X[/math]. [math]X^Y[/math] is not empty because >>15041040
, so now let [math]f[/math] be an element of [math]X^Y[/math] then [math]f[/math] is a function from [math]Y[/math] to [math]X[/math] but [math]f[/math] is also in [math]Y^X[/math] so [math]f[/math] is also a function from [math]X[/math] to [math]Y[/math], so we have [math]X=\operatorname{dom}f=Y[/math].