Without doubt recurrent reasoning in mathematics and inductive reasoning in physics rest on different foundations, but their march is parallel, they advance in the same sense, that is to say, from the particular to the general.
Let us examine the case a little more closely.
To demonstrate the equality
a + 2 = 2 + a
it suffices to twice apply the rule
(1) a + 1 = 1 + a
and write
(2) a + 2 = a + 1 + 1 = 1 + a + 1 = 1 + 1 + a = 2 + a.
The equality (2) thus deduced in purely analytic way from the equality (1) is, however, not simply a particular ease of it; it is something quite different.