why, Sets??

So… What are sets?!!

Sets are objects that other object can be identified with them, if they follow and fall in the general concept that they describe. like when i say cars you may think of Ford or Lamoborgini, but one thing is clear, you thought of a car not some random airplane nor of ducati. now since we talking maths, sets are collection of object like numbers, variables and other sets.

if you ever heard of set and thought “you know what? The elements in this set arent quite clear to me” as of like “set of top three best programming language??”. me personally would say python, java script and c++ but if you ask someone else they might say completely different languages. So what im trying to say is that, you must be able to say if this particular object or number or variable belongs to this set. If you cant, then that is not a valid set, and believe me dont think about it more…

Representation

$A=\{1,2,3,4,5,6\}$ general rules to be followed:

• Elements, objects and members of sets are refer to the same thing
• Sets are usually denoted by capital letters. as shown above. eg: A, B, X
• Elements in the set are represented by small letters $Z=\{a,b,c,d,x\}$

Example of Sets predefined in Mathematics

Note

... this is denoted as continues forever

N : the set of all natural numbers $N=\{1,2,3,4,5,6,...\}$

Z : the set of all integers $Z=\{...,-3,-2,-1,0,1,2,3,...\}$

Q : the set of all rational numbers $\mathbb{Q}=\left\{\dots ,-2,-\frac{3}{2},-1,-\frac{1}{2},0,\frac{1}{2},1,\frac{3}{2},2,\dots \right\}$

R : the set of all real numbers $\mathbb{R}=\{\dots ,-\pi ,-2,-\sqrt{2},-1,-0.5,0,0.5,1,\sqrt{2},2,\pi ,\dots \}$

Why, Sets??

we come back to the same question that we started all of this with “Why Sets??”. as of why it is the first chapter of class 11, Because it is the building block to higher concepts to be taught. Or as of like “why sets are important to even know of and learn?” because sets are very cool and are used in other concepts such as functions, geometry, and probability.

Next up

set-representation subset-power-Universal-set Venn-Diagram

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These notes are for understanding concepts only and are not a replacement for your textbook or school classes.