By inspection just means "go look at it". It is usually used when examining a finite set. For example, [math]\href{/cs2800/wiki/index.php/Enumerated_set}{\{1,2,3\}} \href{/cs2800/wiki/index.php/%5Csubseteq}{\subseteq} \href{/cs2800/wiki/index.php/Enumerated_set}{\{1,2,3,4\}} [/math] means "clearly [math]1 \href{/cs2800/wiki/index.php/%5Cin}{\in} \href{/cs2800/wiki/index.php/Enumerated_set}{\{1,2,3,4\}} [/math], [math]2 \href{/cs2800/wiki/index.php/%5Cin}{\in} \href{/cs2800/wiki/index.php/Enumerated_set}{\{1,2,3,4\}} [/math], and [math]3 \href{/cs2800/wiki/index.php/%5Cin}{\in} \href{/cs2800/wiki/index.php/Enumerated_set}{\{1,2,3,4\}} [/math].
Of course, when you write "by inspection" in a proof, you had better go do the inspecting!
