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Functions

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Definition
Let A and B be two subsets of ℝ
A relation from A to B is a rule which assigns a member of B to each member of A.
Definition
Let A and B are two subsets of ℝ
A function from A to B is a rule which assigns a unique member of B of each number of A.

About Padmal's Blog

This is my very first blog. Learning and implementing about blogging and discovering it's trends, basically this blog will help anyone out with Mathematics, Python Programming Fundamentals at the university level.
Mathematics will cover Logic and Set Theory [Propositions, Quantifiers, Techniques of Proof, Sets, Relations, Functions], Real Analysis [Intervals, Supremum and Infemum, Completeness Axiom, Limit of a Function, Differentiability, Rolle’s Theorem, L’ Hospital’s Rule, Sequences, Convergence of Series: Ratio Test, Comparisons Test, Limit Comparison Test, Maclaurine’s Integral Test; Taylor’s Series, Integration of Continuous Functions, Definite and Indefinite Integrals], Complex Numbers, Vectors, and Matrices [Algebra of Complex Numbers, De Moriver’s Theorem, Argand Diagram, Vector Algebra, Scalar Triple Product, Vector Triple Product, Line and Plane, Matrix Algebra, Echelon Forms, Rank, Determinants, Eigen Values, Spectral Radius, Matrix Norms: Maximum Row Sum, Maximum Co…

Intervals

Defenition
Let A ≤ R; A is said to be an interval if following condition is satisfied.

If a, b ∈ A with a < b, then
a < x < b ⇒ x ∈ A

Eg: A = {1, 2, 3, 4}
2, 3 ∈ A & 2 < 2.5 < 3 & 2.5 ∉ A

Therefore A is not an interval

Inequalities

Definition
ℝ+ = {a | a ∈ ℝ and a is located to the R.H.S. of 0 in the number line}
ℝ- = {a | a ∈ ℝ and a is located to the L.H.S. of 0 in the number line}
{0} = The single point 0
Then, ℝ = ℝ- ∪ {0} ∪ ℝ+

Irrational Numbers

In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers. Informally, this means that an irrational number cannot be represented as a simple fraction. Irrational numbers are those real numbers that cannot be represented as terminating or repeating decimals. As a consequence of Cantor's proof that the real numbers are uncountable(and the rationals countable) it follows that almost all real numbers are irrational.
Note: ∃ a (There is...)∃ a1, a2, a3 ... (There are...)

Creating Tabs in Blogger

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In Blogger, there is no inbuilt option to create tabs. So we're using a tricky way to create tabs. It is actually Labels that are playing the role of tabs here and we're simply displaying those labels in the form of tabs. I think now you get the picture of what's going to happen here. I'll bring it down step by step.

Edit CSS in Blogger!!!

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Before getting started, let me introduce you to CSS.CSS is Cascading Style Sheets which is a style sheet language used for describing the look and formatting of a document written in a markup language. While most often used to change the style of web pages and user interfaces written in HTML and XHTML. Along with HTML and JavaScript, CSS is a cornerstone technology used by most websites to create visually engaging webpages, web applications and user interfaces for many mobile applications.

How to make a Blog!!!

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Blogging is Art. You'll get what I'm saying once you root yourself into blogging. Blogging enables you to post almost anything you want to share with the world. You can write a novel, your own short story or your autobiography. It could be anything as long as you want to share it.
How to blog?
First you need to have the need to create a blog. Start simple. There are free blogging sites all over the internet and here I've listed a few for you to try. And in this blog, I'm focusing on Blogger by Google. It's simple and easy to use. I mean all of them. The main purpose is to have something that belongs to you in the Internet.
1. Blogger
2. Penzu
3. Square Space
4. Svbtle
5. Tumblr
6. Webs
7. Weebly
8. Wix
9. WordPress
10. Blog

University of Moratuwa

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Faculty of Engineering :::
The Faculty of Engineering is the largest faculty in the University of Moratuwa, comprising 12 academic departments, over 200 academic staff and around 3500 undergraduate and post-graduate students. The Faculty at present offers Bachelor of the Science of Engineering degree in 9 disciplines, Bachelor of Design degree in Fashion Design and Product Development and Bachelor of Science degree in Transport and Logistics Management. In addition, the Faculty offers a large number of post-graduate degrees leading to Master of Science, Master of Engineering, Master of Philosophy, Master of Business Administration and Doctor of Philosophy.

Star Patterns in C

Two pyramids in two for loop
When using two for loops separately inside the main for loop to create this pyramid, it takes a lot of memory and time to compile. So it is efficient in every way to use only one for loop and an if statement inside the main for loop.
Output :
* ** *** **** *** ** *

Bubble Sort

Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that works by repeatedly stepping through the list to be sorted, comparing each pair of adjacent items and swapping them if they are in the wrong order. The pass through the list is repeated until no swaps are needed, which indicates that the list is sorted. The algorithm gets its name from the way smaller elements "bubble" to the top of the list. Because it only uses comparisons to operate on elements, it is a comparison sort. Although the algorithm is simple, it is too slow for practical use, even compared to insertion sort.