find a number between 3.24 and 3.241 if there is one. is there is no number between them,explain why not.

the smallest real number that is greater than 2?explain or why not in your own words.

Results 1 to 6 of 6

- Apr 25th 2008, 01:29 PM #1

- Joined
- Apr 2008
- Posts
- 3

- Apr 25th 2008, 01:31 PM #2

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

- Apr 25th 2008, 01:57 PM #3

- Apr 25th 2008, 02:58 PM #4

- Apr 25th 2008, 03:34 PM #5

- Joined
- Dec 2007
- Posts
- 131

If you have two distinct real numbers $\displaystyle x$ and $\displaystyle y$, you can ALWAYS find a number $\displaystyle \frac{x+y}{2}$ where $\displaystyle x<\frac{x+y}{2}<y$. For your example, $\displaystyle 3.24<\frac{3.24+3.241}{2}<3.241 \implies 3.24<3.2405<3.241$.

- Apr 25th 2008, 03:43 PM #6

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 12,028
- Thanks
- 848

Hello, luzerito!

Find a number between 3.24 and 3.241. If not, explain.

Given two different numbers, their__average__is always between them.

For example: .$\displaystyle \frac{3.24 + 3.241}{2} \:=\:3.2405$

. . and: . $\displaystyle 3.2400 < 3.2405 < 3.2410$

The smallest real number that is greater than two.

If you say: .$\displaystyle 2\frac{1}{10} = 2.1$ is the smallest,

. . we can say: .$\displaystyle 2\frac{1}{1,\!000} = 2.001$ is smaller,

. . then you can say: .$\displaystyle 2\frac{1}{100,\!000} = 2.00001$ is even smaller . . . etc.