[snip]
...
would fail if the primes included 1. A slightly less illuminating but
mathematically correct reason is noted by Tietze (1965, p. 2), who
states "Why is the number 1 made an exception? This is a problem that
schoolboys often argue about, but since it is a question of
definition, it is not arguable."
It's exactly this sort of "logic" that gets people into trouble. If
the entity doing the 'defining' happens to be dead wrong, then this
sort of thing just leads to totalitarian governments, as then you can't
question the basic tenets without serious consequence. That's not to
say that your 'results' of questioning the tenets are themselves
correct or incorrect, just that you (or any scientist or mathematician)
should be able to ask questions about any proof - or axiom thereof -
that leads to increased wisdom. (A 'Broadsword +1 [WIS] of the
Mathematician', anyone?)
In any case, this is way off topic.
[snip - other stuff deleted to save electrons]
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