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This derivation is itself only valid if you accept the rules
of logic. You would have to postulate something like:
If (0) holds and
(1) and (2) hold, then the successor of zero is a natural number (one
is just a convenient name for the successor of zero).
you need more math help ?
You could go on
like this forever, proposing higher-level rules and setting them down
as further assumptions, but no end is in sight. (This comes from a
classic Lewis Carroll dialogue.) learn more on math forum.
This derivation is itself only valid if you accept the rules
of logic. You would have to postulate something like:
If (0) holds and
(1) and (2) hold, then the successor of zero is a natural number (one
is just a convenient name for the successor of zero).
you need more math help ?
You could go on
like this forever, proposing higher-level rules and setting them down
as further assumptions, but no end is in sight. (This comes from a
classic Lewis Carroll dialogue.) learn more on math forum.
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