need help for Analysis Class (Topic: Measure Zero)

[supermer]

Could anyone help me with this question?

Show that Rational # intersect with [0,1] is of measure zero in R.

here is what i know, we know that Rational # intersect with [0,1] is countable by the property of Rational #
And i believed that any countable is of measure zero. But I don't know how to show that any countable set is of measure zero

Thanks in advance

 

[oboeguy]

You're asking me to remember too far back (ugh, like 8 years?). My intuition is that a proof by way of contradiction is in the offing (duh, like I helped a lot there). Take our your copy of Rudin or hit the library to find one and hop to it. I'm sure you're right about that countability argument, btw.

 

[Mday]

• show that any countable set is of measure zero (work with definition)
• show that the set of rational numbers is countable
• show that the intersect is countable
• concluding statement