- #1
sinClair
- 22
- 0
Hi everyone. I'm a math student still learning to do
proofs. Here is a problem I encountered that seems easy but
has me stuck.
1. The problem statement, all variables and given/known
data
Let a be a positive rational number. Let A = {x e Q (that
is, e is an element of the rationals) | x^2 < a}. Show that
A is bounded in Q. Find the least upper bound in R of this
set.
None.
So I want to show that there exists an M such that x < or =
to M for all x in A.
So for all x in A, x^2<a.
=> x < (a/x) if x>0 or x > (a/x) if x < 0
So it seems like I find an upper bound for x if x is
positive and a lower bound for x if x is negative but what
havn't acounted for the other cases.
Thanks for your help.
proofs. Here is a problem I encountered that seems easy but
has me stuck.
1. The problem statement, all variables and given/known
data
Let a be a positive rational number. Let A = {x e Q (that
is, e is an element of the rationals) | x^2 < a}. Show that
A is bounded in Q. Find the least upper bound in R of this
set.
Homework Equations
None.
The Attempt at a Solution
So I want to show that there exists an M such that x < or =
to M for all x in A.
So for all x in A, x^2<a.
=> x < (a/x) if x>0 or x > (a/x) if x < 0
So it seems like I find an upper bound for x if x is
positive and a lower bound for x if x is negative but what
havn't acounted for the other cases.
Thanks for your help.
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