The largest number

I make a challenge:

Notwithstanding that there are many sorts of number, I can yet
truthfully claim that the largest number is 6.
To those in the know, this claim might seem to issue from a
mathematical constructivism (also known as finitism), where a
mathematical statement must be shown to be constructed 'in practice',
and not merely be assumed to exist by the extrapolations of theory. But
finitism omits a quite simple axiom which underpins the principle of an
act being made 'in practice', the inclusion of which would clarify the
constructivist stance. I will not reveal that axiom here, but, on the
shaky assumption that mathematicians are interested in these sort of
things, present it as a challenge:

My challenge is this -
The constructivist stance to mathematics is a strong stance to take. I
challenge anyone to demonstrate that 6 is not the largest number.

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