Successors no common factors easier to learn

That successors, N, N’, have no common factor is easier to learn than there are infinitely many primes.  It is easier to learn in the sense that we can understand the reason why it is true more directly.

(N’-N)/q = N’/q – N/q = j-i

where j and i are naturals.

But also

(N’-N)/q = 1/q

so

j-i = 1/q

this can’t be.

The statement of the lemma suggests how to go about the proof.  Whereas with the infinitely many primes, there is no suggestion of how to start the proof.  Thus it is mysterious.  Thus it is harder to learn.  Thus it is harder to remember.

Successors have no common factor is easier to learn, prove and remember.

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About New Math Done Right

Author of Pre-Algebra New Math Done Right Peano Axioms. A below college level self study book on the Peano Axioms and proofs of the associative and commutative laws of addition. President of Mathematical Finance Company. Provides economic scenario generators to financial institutions.
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