Welcome to our community

Be a part of something great, join today!

Number Theory Proof of the Division Algorithm

matqkks

Member
Jun 26, 2012
74
In many books on number theory they define the well ordering principle (WOP) as:
Every non- empty subset of positive integers has a least element.
Then they use this in the proof of the division algorithm by constructing non-negative integers and applying WOP to this construction. Is it possible to apply the WOP to a subset of non-negative integers? Am I being too pedantic?
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
It's rather obvious isn't it? "Applying the WOP to a subset of non-negative integers" would simply mean that, given X, a subset of the non-negative integers, any subset of X has a least member. And that is true because any subset of X is also a subset of the non-negative integers.

If that is not what you mean then please explain what you mean by "apply the WOP to a subset of non-negative integers".
 
Last edited:

matqkks

Member
Jun 26, 2012
74
Yes of course. I just had a senior moment.
Thanks.
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
There are those of use who live in "senior moments"! We are called "seniors".
 
Last edited: