Take the 2-minute tour ×  Learning about proof by induction, I
take it that the first step is always something like "test if
the proposition holds for $n = \textrm{[the minimum value]}$"
Like this:  Prove that $1+2+3+...+n = \frac{n(n + 1)}{2}$ for
all $n \ge 1$.  Test it for $n = 1$:  $$n = \frac{n(n + 1)}{2}
\implies 1 = \frac{2}{2}\textrm{, which holds.}$$  * The rest of
the proof goes here *  So, I do it all the time (like a
standard). But I never really thought about why. Why do I do
such test? I can see that if the test does not hold, it cannot
be proven by induction, I guess. But is there another reason we
do this?  share|improve this question seems like if you want to
prove something from here to infinity checking "here" is a good
first step... but I don't know a formal name for that. –  Grady
Player Dec 1 '13 at 1:12 Here - "the least element" maybe
@GradyPlayer. Honestly I think that you couldn't comprehensively
conclude that the expression is true for the entire set of
numbers. –  Zhoe Dec 1 '13 a