# Bounds in real numbers

Could you help me some with real numbers, please... Is a subset of $[-1,\frac 5 2)$ equal to $\{x:-1\leq x<\frac 5 2\}$? How can I explain this equation with mathematical terms by the way...? I mean, in verbal. THANK YOU for reading...

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I'm not sure what you mean, but it is true that $[-1,5/2) = \{x \mid -1 \leq x < 5/2\}$. – Stefan Smith Feb 22 '12 at 1:57
Thank you very much for editing my post, yes, I'm working with real numbers and bounds now... – Kerim Atasoy Feb 22 '12 at 2:14

I'm not sure anyone can answer your question as it's worded right now, since there seems to be some mixed-up terminology in there. So I will just try to explain how the interval notation like "$[-1,5/2)$" is used.

So, with your example, the following three sentences all mean exactly the same thing:

• $x$ is in $[-1,5/2)$.
• $-1 \leq x < 5/2$.
• $x$ is greater than or equal to $-1$, but less than $5/2$.

Intervals like your example are sets, or collections of things. A set is said to contain the things in it, and those things are called the elements or members of that set. The interval $[-1,5/2)$ is the set containing all real numbers that are greater than or equal to $-1$ but less than $5/2$. So for example, we could say

$0.3$ is an element of the set $[-1,5/2)$.

Or, more simply,

$0.3$ is in $[-1,5/2)$.

In the standard interval notation, a square bracket means that you include the number next to the bracket in the set, and a round bracket means that you don't. So the interval $(5,7)$ contains neither $5$ nor $7$: it only contains those numbers strictly greater than $5$ and strictly less than $7$. So, if $x$ is in $(5,7)$, then $5 < x < 7$. (Note: brackets are used for lots of other things in math; here I'm using $(5,7)$ as an interval, but elsewhere it might be an ordered pair.)

Now, a subset of some set $S$ is just another set that happens to only contain elements that are also elements of $S$. So, the set containing all European math teachers is a subset of the set containing all Europeans. Another example: $[0,2]$ is a subset of $[-1,5/2)$. Now $2$ is a number that is in both $[0,2]$ and $[-1,5/2)$. The number $-1/2$, on the other hand, is not a member of $[0,2]$, but still a member of $[-1,5/2)$.

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I understand... Thank you very much for your EXTREMELY valuable help here, Sir. – Kerim Atasoy Feb 22 '12 at 2:43

The interval $[-1,5/2)$ consists of all real numbers between -1 and 5/2 (including $-1$, but excluding $5/2$) - or $\{ x| -1 \le x < 5/2\}$ as you have indicated. This forms a set, which we denote $A$. A subset is another set $B$ such that all the elements of $B$ are also in $A$. For example the sets $(-1,1),[0,1/2),(1/4,1/2]$ are all subsets of $A$

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Thank you, Juan, I just recognized both these last replies, that's why I'm sending my appreciations so late... :) – Kerim Atasoy Feb 22 '12 at 2:34

$[-1, 5/2)$ is, by definition, the set of $x$ such that $-1 \le x < 5/2$. So probably you should not have the word subset in your sentence there.

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Thank you very much, Sir. You've enlightened me very much on this. – Kerim Atasoy Feb 22 '12 at 2:19