Thread: need help, problem sect(1-3#17) "an introduction to analyssis"

17. let a>1, and r a possitive irrational number. Let
A={a^x|x is a positive rational number <r}
B={a^x|x is a positive rational number >r}
show that:
a) the swet A is bounded above, and the set B is bounded below.
b) if s belong to A and t to B, then s<t.

Originally Posted by mancillaj3

17. let a>1, and r a possitive irrational number. Let
A={a^x|x is a positive rational number <r}
B={a^x|x is a positive rational number >r}
show that:
a) the swet A is bounded above, and the set B is bounded below.
b) if s belong to A and t to B, then s<t.

A good way to show that a set is bounded above is to show a number that is an upper bound! You know that x cannot be larger than r. What does that tell you about a^x?