• Apr 25th 2008, 01:29 PM
luzerito
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.
• Apr 25th 2008, 01:31 PM
ThePerfectHacker
Quote:

Originally Posted by luzerito
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.

Take 3.2405
• Apr 25th 2008, 01:57 PM
Jhevon
Quote:

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

this does not exist. you are asking for a number in the interval $\displaystyle (2, \infty)$. this is a subset of $\displaystyle \mathbb{R}$ that has no least element. Meaning, any number you choose in there, you can find a smaller number in there.
• Apr 25th 2008, 02:58 PM
Mathstud28
Quote:

Originally Posted by luzerito
find a number between 3.24 and 3.241. if not explain

the smallest real number that is greater than two?explain not

i hope you can help asa thanks

The smallest real number greater than two would be "$\displaystyle \lim_{x\to2^{+}}x$" note the ""...you cant have this...you name a number I will name a number smaller...it is why non-included endpoints in a domain cannot have endpoint extrema
• Apr 25th 2008, 03:34 PM
xifentoozlerix
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
Soroban
Hello, luzerito!

Quote:

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: . $\displaystyle 3.2400 < 3.2405 < 3.2410$

Quote:

The smallest real number that is greater than two.
There is no smallest number 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.