- #1

PcumP_Ravenclaw

- 106

- 4

Member warned about posting homework problems in non-homework sections

Show that there are infinitely many rational numbers ## \frac{a +m*c}{b + m*d} ## between the two rational numbers ## a/b## ##c/d ##. m is any positive integer.

My attempt:

first make common denominator

##

\frac{a*d}{b*d}##

##\frac{c*b}{d*b}

##

all numbers going from ##a*d## to ##c*b## divided by ##b*d## is in this interval. but these are finite so we have to increase the resolution. say multiply numerator and denominator by 1000 so now ## a*d*1000 ## to ## c*b*1000 ## divided by ## b*d*1000 ## .

It can be 100000 or anything very large say multiplied to infinity. how do I write this mathematically?

My attempt:

first make common denominator

##

\frac{a*d}{b*d}##

##\frac{c*b}{d*b}

##

all numbers going from ##a*d## to ##c*b## divided by ##b*d## is in this interval. but these are finite so we have to increase the resolution. say multiply numerator and denominator by 1000 so now ## a*d*1000 ## to ## c*b*1000 ## divided by ## b*d*1000 ## .

It can be 100000 or anything very large say multiplied to infinity. how do I write this mathematically?