Thread: Prime Numbers Book View Single Post
2020-10-11, 22:26   #13
Nick

Dec 2012
The Netherlands

2×7×113 Posts

Quote:
 Originally Posted by paulunderwood The man in the street with a little interest in primes and testing Please detail what the errors are so that I can fix them.
Feedback on version dated 11 October 2020 (wow you've written a lot!)
p5 The proof that root 2 is irrational relies on the uniqueness of prime factorization.
As this is a special property of the integers (not true in all number systems), I would at least mention it.
p6 Ordinary sets are unordered and may not have repeating elements (this is so that they correspond with properties - if you select all objects satisfying a certain condition, you want what you get to be a set). Orderings and multisets can be constructed from ordinary sets if needed (in fact, so can everything in mathematics).
p6 "subtracting all elements of one set from another" sounds confusing to me, as if you are calculating x-y for each x in the first set and y in the second. I would consider "removing"
p7 The group axioms $$e\circ g=g$$ needs to be $$g\circ e=g$$, or state it and the next one both ways around.
p7 under multiplication the units of a commutative ring with 1 form an abelian group, but these are not all the elements of the ring (except in the trivial case where the ring has just 1 element).
p8 If you want to be able to relax condition 11 then you need to write condition 12 both ways around!
p8 A field is also required to have 1 not equal to 0.
I'm out of time now - I'll look again in the week.