Question

If a is rational and b is irrational, is ab necessarily irrational? (Careful!)

Answer 1

we need a contradiction

Answer 2

may be, not really

Answer 3

u can use that in one case

Answer 4

b=baa^(-1) is irrational
b=aba^(-1)=(ab)(a^(-1))
a is rational => a^(-1) is rational (assuming a doesn't =0)
but for b to be irrational that means ab has to be irrational

Answer 5

if a = 0 then ab is rational. Assume a not= 0 and ab is rational then ab/a is rational too, so b = ab/a has to be rational.

Answer 6

but 0 is rational
0*b is rational

Answer 7

hey nikita do u have this book? ny Michael Spivak?

Answer 8

by*

Answer 9

definitely no )

Answer 10

okay ur approach is right

Answer 11

two cases:
if a = 0
if a is not 0

Answer 12

wat is title of this book?

Answer 13

Calculus by Michael Spivak

Answer 14

http://books.google.com/books?id=7JKVu_9InRUC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

Answer 15

thats right, its a good book

Answer 16

Are u really want to learn it ?

Answer 17

what do u mean?

Answer 18

I mean calculus and this boot in particular