Comment on Proofs, Implications, and Models

Thu, 01 Nov 2012 15:50:36 GMT

In fancy math-talk, we can say apples are a semimodule over the semiring of natural numbers.

You can add two bunches of apples through the well-known "glomming-together" operation.

You can multiply a bunch of apples by any natural number.

Multiplication distributes over both natural-number addition and glomming-together.

Multiplication-of-apples is associative with multiplication-of-numbers.

1 is an identity with regard to multiplication-of-apples.

You could quibble that there is a finite supply of apples out there, so that (3 apples) + (all the apples) is undefined, but this model ought to work well enough for small collections of apples.

Discuss