All Questions
Tagged with well-orders number-theory
7
questions
1
vote
0
answers
108
views
Discussion of Exercise 9, section 4 on page 35 of Munkres’ Topology 2E.
In Exercise 9, section 4 on page 35 of Munkres’ Topology 2E, the problem is stated as follows.
Exercise 4.
(a) Show that every nonempty subset of $\mathbb{Z}$ that is bounded above has a largest ...
- 307
0
votes
1
answer
146
views
Well ordering principle for mini tetris
Prove using well ordering principle that for all $n\ge 0$, the number $T_n$ of tilings of a $n \times 2$ tetris board is : $\frac{3^{n+1} + (-1)^{n}}{4}$
I am using MIT OCW to learn this on my own.
...
- 439
1
vote
1
answer
80
views
I don't understand how this set can be contained in $\Bbb N$
In my lecture notes there is a proof for the division algorithm which sets $S=\{a-xb|x\in \Bbb Z, a-xb \geq 0 \}$ then says $S\subset\Bbb N$ so we can use the well ordering principle.
There's a ...
- 2,815
2
votes
3
answers
175
views
Example of Set which possesses well ordering property other than Integers
During Studying Elementary Number theory I had encountered in property called as well ordering property which tell every nonempty set of natural number has least element.
I had interested in is such ...
- 6,653
-1
votes
1
answer
33
views
Prove that $p\le x<p+1$ by well ordering property [closed]
by using well ordering property prove that if $x$ is a positive real number then there exist unique integer $p\ge0$ such that $p\le x<p+1$.
- 3
0
votes
2
answers
101
views
Show that the set {1/6, 1/7 , 1/8,.....} does not have a least element
Show that the set $\{\frac 16,\frac 17 ,\frac 18,\dots\}$ does not have a least element and conclude that no set containing this set is well ordered.
I am not sure how can I show this ... The set ...
- 619
13
votes
2
answers
9k
views
Prove that there is no positive integer between 0 and 1
In my textbook "Elementary Number Theory with Applications" by Thomas Koshy on pg. 16, there is an example given just after the well ordering principle:
Prove that there is no positive ...
- 1,005