Treatment of Inequalities

  • Thread starter Ronnin
  • Start date
  • #1
168
0
I've been playing around with some proofs and find myself relearning how I do my mathmatical thinking. Just a general question regarding how to handle something like this.

0<a<b So a and b must be positive
a/2 <b I just divided one side by two instead of "dividing through" like you would an equation. The statement is still true, would this be a legal manipulation (for whatever reason)?
 

Answers and Replies

  • #2
Char. Limit
Gold Member
1,204
14
I've been playing around with some proofs and find myself relearning how I do my mathmatical thinking. Just a general question regarding how to handle something like this.

0<a<b So a and b must be positive
a/2 <b I just divided one side by two instead of "dividing through" like you would an equation. The statement is still true, would this be a legal manipulation (for whatever reason)?
Well, you might have to justify it, but it's still certainly true, because for positive b:

b/2 < b

And by dividing all sides of the equation by 2, you get...

0<a/2<b/2<b --> 0<a/2<b
 

Related Threads on Treatment of Inequalities

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
534
  • Last Post
Replies
6
Views
678
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
821
  • Last Post
Replies
1
Views
2K
Top