a little help please

**luzerito** · April 25th 2008, 01:29 PM

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.

**ThePerfectHacker** · April 25th 2008, 01:31 PM

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

**Jhevon** · April 25th 2008, 01:57 PM

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 $(2, \infty)$ . this is a subset of $\mathbb{R}$ that has no least element. Meaning, any number you choose in there, you can find a smaller number in there.

**Mathstud28** · April 25th 2008, 02:58 PM

Originally Posted by luzerito

please i need help
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 " $\lim_{x\to2^{+}}x$ " 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

**xifentoozlerix** · April 25th 2008, 03:34 PM

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

**Soroban** · April 25th 2008, 03:43 PM

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

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

The smallest real number that is greater than two.

There is no smallest number greater than two.

If you say: . $2\frac{1}{10} = 2.1$ is the smallest,
. . we can say: . $2\frac{1}{1,\!000} = 2.001$ is smaller,
. . then you can say: . $2\frac{1}{100,\!000} = 2.00001$ is even smaller . . . etc.

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a little help please