Question

NOTATION: What does:= mean?

Answer 1

equated?

Answer 2

assign?

Answer 3

"is defined to be"

Answer 4

What's the apparent difference between "=, =, and = bar then?

Answer 5

i havent seen the apostrophe one before
but = to and equivalent or congruent for 3 bars

Answer 6

lol what kinda questions are these!

Answer 7

@dan815 question of notation

Answer 8

I just think it is stupid how I always see a mix of :=, =, and = bar when all three symbols seem the same to me.

Answer 9

:= means "is defined to be"
= means "is equal"
\(\equiv\) means always equal

Answer 10

lol interesting...

Answer 11

So it would be correct to say that @FutureMath Professor ≡ Smart, @dan815 = smart?

Answer 12

heh

Answer 13

For example,
\[e:=1+\frac11+\frac1{1\times2}+\frac1{1\times2\times3}+\cdots\]\[2x+3=x+4\]\[(a+b)(a-b)=a^2-b^2\]

Answer 14

The last one should be \(\equiv\) sorry

Answer 15

What's the difference in notation in your 2nd and 3rd example?

Answer 16

no you got that wrong it should be
dan815:=smart

Answer 17

lol

Answer 18

I said the last one should be \(\equiv\) sorry for typo

Answer 19

I know, but why would they have different signs then? look like the same cconcept to me

Answer 20

to be honest this kind of stuff i see in programming a lot thats about it

Answer 21

equal sign is used for equations, equivalent sign is used for identities, though we always mix it

Answer 22

in maple
you use := for assigning equations
like eq1:=x^2+y^2=0

Answer 23

lolz this is not maple

Answer 24

That's because an identity implies an equality

Answer 25

@terenzreignz yep agree

Answer 26

or equivalent sign makes you to compare like terms instead of solving an equation with 5 unknowns.

Answer 27

makes sense... but why did the dog cross the road

Answer 28

@dan815 , what's the best abstract algebra book?

Answer 29

for example,
\[x^2+kx+1\equiv(Ax+B)^2\]

Answer 30

I know a good one wait.. zzrocker sent me one

Answer 31

This 4-unknown equation may be hard to solve, but since there is an equivalent sign in the middle, it will be solvable

Answer 32

Oi Lau, improper use of the identity sign XD

Answer 33

@terenzreignz lolz it's not only for identities

Answer 34

I use CAA by Gallian, do you think that is any good?

Answer 35

do you want intro to abstract algebra

Answer 36

A First Course In Abstract Algebra-Jb Fraleigh, 7Ed(2003).pdf

Answer 37

I'll go on the pirate bay and look it up

Answer 38

wait u need to do start with set theory first

Answer 39

I know everything about that, I learned that in 8th grade haha

Answer 40

then do group theory

Answer 41

Ok

Answer 42

these are all pretty different though u can just start with that book intro to abs alg

Answer 43

im just passing on advice i got from zzrocker

Answer 44

Oh yeah... triple bar is also used for congruence modulo...

Answer 45

I scared zzrocker off the website he got too intimidated by me lmao

Answer 46

DAN!!!!!!!!!!!!!!!!!!!!!!!!!!! GUESS WHAT!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 47

You know all the Calculus three help you gave me over the summer while I was "preparing for class"

Well...
:)
http://gyazo.com/149b9e0b736f60a4caacf1fe96e851b0.png

Answer 48

ya it wont let me upload that big of a file

Answer 49

@FutureMathProfessor So now do you understand the concept of definition sign, equal sign and equivalent sign? If not, I'll explain it again.

Definition sign is used for defining something.
Equals sign is used for declaring that two things are equal, usually used in equations.
Equivalent sign is used for declaring that two things are ALWAYS equal, used in identities or equations that require comparing like terms.

Another use of the equivalent sign is the mod function, for example, \(8\equiv2\mbox{(mod 3)}\).

Answer 50

and good job! im happy

Answer 51

Guys, another quick question I was asked that is going to be on the first exam of my abstract algebra class.

Determine the one's digit of 3^8888 without using a calculator

Answer 52

As if there's a calculator that can handle that XD

Answer 53

lol