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# Announcement

Hi all!
I know some friends, who don’t know what mathematics in real is, always blame me for the language of the blog. It is very complicated and detailed. I understand that it is. But MY DIGITAL NOTEBOOK is mainly prepared for my study and research on mathematical sciences. So, I don’t care about what people say (SAID) about the

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content and how many hits did my posts get. I feel happy in such a way that MY DIGITAL NOTEBOOK has satisfied me at its peak-est level. I would like to thank WordPress.com for their brilliant blogging tools and to my those friends, teachers and classmates who always encourage me about my passion. For me the most important thing is my study. More I learn, more I will go ahead. So, today (I mean tonight) I have decided to write some lecture-notes (say them study-notes, since I am not a lecturer) on MY DIGITAL NOTEBOOK. I have planned to write on Group Theory at first and then on Real Analysis. And this post is just to introduce you with some fundamental notations which will be used in those study-notes.

# Notations

Conditionals and Operators
$r /; c$ : Relation $r$ holds under the condition $c$.
$a=b$ : The expression $a$ is mathematically identical to $b$.
$a \ne b$ : The expression a is mathematically different from $b$.
$x > y$ : The quantity $x$ is greater than quantity $y$.
$x \ge y$ : The quantity $x$ is greater than or equal to the quantity $y$.
$x < y$ : The quantity $x$ is less than quantity $y$.
$x \le y$ : The quantity $x$ is less than or equal to quantity $y$.
$P := Q$ : Statement $P$ defines statement $Q$.
$a \wedge b$ : a and b.
$a \vee b$ : a or b.
$\forall a$ : for all $a$.
$\exists$ : [there] exists.
$\iff$: If and only if.
Sets & Domains
$\{ a_1, a_2, \ldots, a_n \}$ : A finite set with some elements $a_1, a_2, \ldots, a_n$.
$\{ a_1, a_2, \ldots, a_n \ldots \}$ : An infinite set with elements $a_1, a_2, \ldots$
$\mathrm{\{ listElement /; domainSpecification\}}$ : A sequence of elements listElement with some domainSpecifications in the set. For example, $\{ x : x=\frac{p}{q} /; p \in \mathbb{Z}, q \in \mathbb{N^+}\}$ $a \in A$ : $a$ is an element of the set A.
$a \notin A$: a is not an element of the set A.
$x \in (a,b)$: The number x lies within the specified interval $(a,b)$.
$x \notin (a,b)$: The number x does not belong to the specified interval $(a,b)$. Standard Set Notations
$\mathbb{N}$ : the set of natural numbers $\{0, 1, 2, \ldots \}$
$\mathbb{N}^+$: The set of positive natural numbers: $\{1, 2, 3, \ldots \}$
$\mathbb{Z}$ : The set of integers $\{ 0, \pm 1, \pm 2, \ldots\}$
$\mathbb{Q}$ : The set of rational numbers
$\mathbb{R}$: The set of real numbers
$\mathbb{C}$: The set of complex numbers
$\mathbb{P}$: The set of prime numbers.
$\{ \}$ : The empty set.
$\{ A \otimes B \}$ : The ordered set of sets $A$ and $B$.
$n!$ : Factorial of n: $n!=1\cdot 2 \cdot 3 \ldots (n-1) n /; n \in \mathbb{N}$

Other mathematical notations, constants and terms will be introduced as their need.

For Non-Mathematicians:
Don’t worry I have planned to post more fun. Let’s see how the time proceeds!