Question

I'm gonna start the following topics in Algebra :-

Algebraic Identities,Indices,HCF of two polynomials,LCM of two polynomials,Quadratic equations,Division of two polynomials,Set,Logarithms & Linear equation in one variable as well as two variables also.

Please tell me which topic should i start first :)

Answer 1

@waterineyes @ParthKohli help plz :)

Answer 2

Start with indices!

Answer 3

sets

Answer 4

No, Set Theory is the bad math.

Answer 5

oh ok

Answer 6

In my view, start with LCM and HCF and Linear equation in one variable...

Answer 7

Indices help you with regularizing how you view the square root and all.

Answer 8

Indices is actually pre-algebra.

Answer 9

Just do as you wish, what do you want to do first @jiteshmeghwal9 ??

Answer 10

yes ! in my view there is also about Indices becoz i m studying in class-8 & my chapter of Linear Equation in one variable has cleared already.

Answer 11

Indices are actually just exponents and powers. You know about exponents and powers, right?

Answer 12

yes

Answer 13

OK, for pop quiz, solve this:\[\rm 2^x = 1024^{4}\]

Answer 14

ok

Answer 15

\[2^x=1024^4\]
\[2^x=(2^{10})^4\]
\[x=4\times10\]

Answer 16

\[2^x=(2^{10})^4\]\[2^x=2^{40}\]\[a^x=a^b \space if \space x=b\]\[x=40\]

Answer 17

Algebraic Identities,Indices,HCF of two polynomials,LCM of two polynomials,Quadratic equations,Division of two polynomials,Set,Logarithms & Linear equation in one variable as well as two variables also.


My favorite order:

1) Indices (numbers only)
2) Linear equation in one variable.
3) Indices (equations like I gave you)
4) Multiplication of polynomials.
5) Factoring linear expressions (HCF and LCM included)
6) Division of two polynomials.
7) Set theory - starting.
8) Factoring (quadratic expressions)
9) Quadratic equations
10) Logarithms

Answer 18

@UnkleRhaukus That question was for Jitesh. :p

Answer 19

@jiteshmeghwal9 How much have you covered amongst the ten topics?

Answer 20

Thanks.

Answer 21

The basic concepts of all of this have been cleared excepting sets :)

Answer 22

& division of two polynomial also

Answer 23

Okay, can I teach you sets here? It's really easy.

Answer 24

sure :)

Answer 25

I will like :)

Answer 26

okay!

A set is just one collection of anything. You define sets by a capital letter, and the elements are written within these brackets: {...}. An example of a set is the following:\[\rm A = \{shirt, trousers, socks\}\]

Answer 27

Are you getting it till now?

Answer 28

yes !

Answer 29

Nice.

Now, I'd teach you about things such as union, intersection and subset.

Union is when you mix elements of two or more sets. Union of two sets is represented by \(\cup\). So let's say that A = {1,2,3} and B = {2,3,4}, then the union is \(\rm A \cup B = \{1,2,3,4\}\)

Answer 30

@nincompoop lol no... it's too early for him to learn about logic!

Answer 31

ok! i gt this till here

Answer 32

Remember that the union of two sets is another set.

Now, the intersection is represented by an ulta U which is \(\cap\). It's the set of common elements.

A = {1,2,3,4} and B = {4,5,6,7}
then
\(\rm A \cap B = \{4\}\)

Answer 33

@nincompoop Just after the union-intersection thing, I'd be teaching him... okay?

Answer 34

Oh yes! I forgot about it. Sorry dude

Answer 35

@jiteshmeghwal9 Do you know about the Venn Diagram?

Answer 36

u mean that if we combine two sets then we will get a new set ???

@ParthKohli

Answer 37

yes !

Answer 38

Yes!

Answer 39

lol

Answer 40

;)

Answer 41

Now, do you know about subsets?

Answer 42

no

Answer 43

If set B is a part of A, then B is a subset of A.

Answer 44

ok ! gt it

Answer 45

This mathematical statement is denoted by:\[\rm B\subset A\]or\[\rm B \subseteq A\]The thing I wrote below means that B is a subset of or is equivalent to A.

Answer 46

i don't understand that B is equivalent to A

Answer 47

If B is equivalent to A, then they have the same elements.

If B = {dog, cat, horse}
and A = {cat, dog, horse}

then they are equivalent because they have the same elements.

Remember that the order has no relation with equivalence of sets.

Answer 48

ok

Answer 49

There is an axiom associated with this.

If \(\rm A \subseteq B\) and \(\rm B \subseteq A\), then \(\rm B= A\)

Answer 50

Do you understand what that means?

Answer 51

not surely :(

Answer 52

If A is a subset of or it is equivalent to B... and if B is a subset of or it is equivalent to A, then B is definitely equivalent to A.

Answer 53

Ok !

Answer 54

Your last lesson:

Answer 55

If \(\rm a \) is an element in set B, then you can say that \(\rm a\) is in \(\rm B\).

This is denoted by \(\rm a \in B\).

Answer 56

Ok ! i gt it :)

Answer 57

u want to say that B={a} then \[\LARGE{a \space \epsilon \space B}\]

Answer 58

Isn't it ?

Answer 59

Yes, but that's not the definition of it. :D

Answer 60

Though, one thing: B = {a} is better when you want to stress out what set B is.

Answer 61

ya ! i was only clearing this to me

Answer 62

Yeah...

If B = {a,b,c} then also \(\rm a \in B\)

Answer 63

So, now I am going to start with the last lesson.

Answer 64

ok !

Answer 65

... in basic set theory.

Answer 66

Defined sets:

Some sets have been defined by certain letters.

You can write the set of integers like \(\mathbb Z\).
Set of real numbers like \(\mathbb R\).
Set of natural numbers like \(\mathbb N\).
Set of complex numbers like \(\mathbb C\)

Answer 67

but one of the video i saw in you tube taught that when we g at higher level we use letter Z to represent complex numbers.

Answer 68

go*

Answer 69

lol, that's something else. Never mind that.

Answer 70

Ok :)

Answer 71

It's the Z-plane which you learn later. It's not set theory.

Answer 72

Is there any other topic left in set theory now ???

Answer 73

And the Z used in set theory looks like this: \(\mathbb Z\) and not this: \(\rm Z\)

Answer 74

Yes, mathematical logic... but never mind that.

Answer 75

Ok ! Thanx a lot :)

Answer 76

You're welcome. :D

Answer 77

Number system?

Answer 78

Oh... the rational numbers and all

Answer 79

two circles of two different elements when intersect their common elements are written in their intersection point.