Proof by contradiction

  • Thread starter zoxee
  • Start date
  • #1
zoxee
37
0
Prove by contradiction that a real number that is less than every positive real number cannot be positive

having troubles with this

could someone give me a small hint to get started?
 

Answers and Replies

  • #2
pasmith
Homework Helper
2,270
876
Prove by contradiction that a real number that is less than every positive real number cannot be positive

having troubles with this

could someone give me a small hint to get started?

Suppose [itex]x > 0[/itex] is such that every positive real number is greater than or equal to [itex]x[/itex]. What then is [itex]x/2[/itex]?
 
  • #3
zoxee
37
0
Suppose [itex]x > 0[/itex] is such that every positive real number is greater than or equal to [itex]x[/itex]. What then is [itex]x/2[/itex]?

I'm sorry but I can't seem to proceed even with this hint :(
 
  • #4
pasmith
Homework Helper
2,270
876
I'm sorry but I can't seem to proceed even with this hint :(

Given that [itex]x[/itex] is a positive real number, is [itex]x/2[/itex] a positive real number?
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
43,010
969
I wouldn't even bother with x/2. Suppose x is positive. Can it then be "less than every positive number"
 
  • #6
berkeman
Mentor
62,893
13,782
Prove by contradiction that a real number that is less than every positive real number cannot be positive

having troubles with this

could someone give me a small hint to get started?

Please check your PMs. The PF Rules require that you show some effort before we offer tutorial help.
 

Suggested for: Proof by contradiction

  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
960
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
5
Views
802
Replies
32
Views
317
Replies
11
Views
4K
  • Last Post
Replies
10
Views
2K
Replies
6
Views
2K
Top