Analysis curious on how to prove!

  • #1

Main Question or Discussion Point

Analysis math help please!?
1. Let E be a nonempty subset of R (real numbers)

Prove that infE <= supE

2. Prove that if a > 0 then there exists n element N (natural) such that 1/n < a < n

3. A subset E of te real numbers R is an inductive set if

i) 1 element E
ii) If x element E then x + 1 element E

A real number is called a natural number if it belongs to every inductive set. The set of natural numbers is denoted by N. Recall that the priciple of mathematical inductions says that if M is any subset of N that is an inductive set then M = N. Show that N = E, where E = {1,2,3,4...}

Any help would be greatly appreciated ! :)
 

Answers and Replies

  • #2
95
0
1. Proof by contradiction.
2. Archimedean Property
 

Related Threads on Analysis curious on how to prove!

  • Last Post
Replies
20
Views
3K
Replies
8
Views
3K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
9
Views
4K
Replies
5
Views
1K
Replies
7
Views
2K
Replies
1
Views
572
Replies
1
Views
541
Top