Hmm. The basis that `1 + 1 = 2' is apparently just that `.\ x = x + 1' is defined as meaning `the successor of x', for some arbitrary definition of `successor'. Sums using natural numbers other than 1 are found by inverting this function and applying it recursively until the number with which we are working is one. I suppose that, at the heart of this, there is the presumption that
one cannot `make new numbers', but that, rather, there is an
infinite series of numbers (why would one need to make more, if
one already has an infinite number of them?), and the `+1'
function is just Gee, maybe those set-theoretical guys are onto something.... And maybe it's time for sleep.... [Reply] |
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