Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Promoted
cakesmckakes
Lv 4
The Density of I in R?
Let a and b both be in Q (rational numbers). Show that for every c>0, that there exists at least 1 irrational number in (a-c, b-c). In other words, show that I is dense in R
1 Answer
Relevance
- kbLv 79 years agoFavorite Answer
By the density of Q, there exists a rational number r such that (a-c) - √2 < r < (b-c) - √2.
Hence, a - c < r + √2 < b - c.
Since r + √2 is irrational, we are done.
I hope this helps!
Still have questions? Get your answers by asking now.