Page 177 - 'Blast_Into_Math

Blast into Math! Analatic nummer theora: ants, ghosts and giants

Because z is a fraction,

1 ≤ p< q, p ∈ N, and q ∈ N.

So, if we can find N ∈ N such that

n
p
<, ∀n> N,
q

then because |x| <p/q ,

p
n
n
n
|x − 0| = |x| < <, ∀n> N.
q
In the definition of limit, this will mean that x converges to 0.
n

Notice that

p
n
q

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