Question

Q

Answer 1

A

Answer 2

spam?

Answer 3

WUH!!!

Answer 4

sorry typo

Answer 5

mouse + keyboard fail

Answer 6

:) we all make them

Answer 7

yep :D

Answer 8

:)

Answer 9

perl, lol!
Is that going to be a tutorial about a set of all rational numbers or something?

Answer 10

maybe i should :)

Answer 11

... elaborate on the question:)

Answer 12

help me define Q , the set of rational numbers

Answer 13

what is an element of Q exactly

Answer 14

Respectively,

1. natural numbers
2. whole numbers (adding 0 to #1)
3. integers (saying negative integers as well)

4. fractions (positive or negative)
that don't have any non-perfect-square square roots, euler number and other irrationals in them.

basically all reals besides irrational numbers.


or do you want something involving crazy scearing notations?

Answer 15

scaring*

Answer 16

Hmmm, I want a well defined set Q , and you gave me
duplicates "1/2 = 2/4 = 3/6 = ... "

Answer 17

did I say that?

Answer 18

you said fractions?

Answer 19

\(\large\color{slate}{ 2.3/4.7 }\) is also a rational

Answer 20

but, I am saying it is everything asides from irrationals.
my best and shortest definition.

Answer 21

http://mathworld.wolfram.com/RationalNumber.html

Answer 22

for smarties. but I am not in that list of ppl

Answer 23

agreed.
You can also mention when two rational numbers are equal, that way your set Q is not full of duplicate numbers

Answer 24

im kinda getting at equivalence classes, thats a better definition of Q

Answer 25

Well, I also find that
\(\large\color{slate}{ Q}\) stands for "quotients"

and that is true, to be most "narrowed" rational number is fraction (saying it is certainly an integer, but to be most percise a fraction).

Answer 26

when someone says they are thinking of the rational number 1/2, there are many ways to represent this rational number. but the number is unique itself

Answer 27

I will say that a/b = c/d iff ad = bc .

Answer 28

that way there is no ambiguity when you look at a fraction (using integers in numerator and denominator) , what rational number you are dealing with

Answer 29

surely

Answer 30

I like that abcd thingy:)

Answer 31

Yes, you can construct rational numbers using integers, which is cool.
From the other direction, if you start by assuming the existence of real numbers, you can define rational numbers in terms of repeating decimals or terminating decimals .

Answer 32

oh, I left out repeat./term. decimals...
btw, what is the latex for a repeating decimal?

Answer 33

And yes, but you don't have to use integers.
you can use decimals to construct rational numbers.

Answer 34

I mean they will becomes integers as \(\large\color{slate}{ 1.2/2.3~~~~--->~~~~12/23}\)

Answer 35

right

Answer 36

(as some say)
A set of all rational number is a combination of different rations of \(\large\color{slate}{ a/b}\) where \(\large\color{slate}{ a}\) and \(\large\color{slate}{ b}\) are integers.

Answer 37

oh I meant if you start with R , the real numbers, you can define rational numbers as the subset of repeating or terminating decimals. For example
.11111... = 1/9
.121212...= 4/33 , etc

Answer 38

well, it is true though, as I said, decimal reduce to integers

Answer 39

and I guess I defined R implicitly as infinite decimals :)

Answer 40

sorry, i meant R = set of all infinite decimal

Answer 41

you can define R in other ways as well

Answer 42

Yes, R is not imaginary. lol jk

Answer 43

:L

Answer 44

wait that is not a laplace I hope

Answer 45

:)

Answer 46

i think theres a nice Latex font for R, C, Q

Answer 47

maybe

Answer 48

1. integers = discrete function
2. rational numbers = relations
3. real numbers = relations involving Euler numbers like \(\large\color{slate}{ \pi}\) and \(\large\color{slate}{ e}\)

I haven't even been a fan of definitions.

Answer 49

or for 3, squares roots too

Answer 50

or other roots

Answer 51

just a question on your comments

Answer 52

you said decimals reduce to rational numbers
1.2 /2.3

what about
.11111... / .121212...

Answer 53

well, those infinite decimals are fractions, in actuallity, aren't they?

Answer 54

I thought perl fanned me at first, but it turned out it was just a notification that he replied to this post haha:P

looks like im going to put the champagne back in the cooler..

Answer 55

right

Answer 56

yeah:P

Answer 57

just checking :)
hi squirrel @Squirrels

Answer 58

\(\large\color{slate}{ \sqrt{2} / \sqrt{8}}\) is rational.

Answer 59

lol

Answer 60

hmm :)

Answer 61

Hey bud, good job with your work. Continue my friends.

Answer 62

it is

Answer 63

right

Answer 64

1/2

Answer 65

duh...:D

Answer 66

so , looks can be deceiving (that is the moral here)

Answer 67

Yes:)
And that is how decimal/decimal is rational too

Answer 68

" don't just take it as it is, play with it! "

Answer 69

When we use a squeeze trm, btw..... for floor function x

Answer 70

I lagged

Answer 71

squeeze term for floor function , explain /elaborate

Answer 72

\(\large\color{black}{ \displaystyle \frac{\lfloor x \rfloor }{x} }\)

Answer 73

thats an interesting function

Answer 74

the limit is 1 as x-> oo ?

Answer 75

for instance,

\(\large\color{black}{ \displaystyle\lim_{x \rightarrow ~{\Large \pm}\infty} \frac{\lfloor x \rfloor }{x} =1 }\) where \(\large\color{black}{ \displaystyle\lfloor x \rfloor }\) is a floor function of x.

but will just take \(\large\color{black}{ \displaystyle\lim_{x \rightarrow ~{\Large }\infty} \frac{\lfloor x \rfloor }{x} =1 }\) for now,

Answer 76

so you can break it down , first consider integer values, then non integer values?

Answer 77

If you take:

\(\large\color{black}{ \displaystyle \frac{x-1}{x}<\frac{\lfloor x \rfloor }{x} < \frac{x}{x} }\)

Answer 78

ohh

Answer 79

I am bringing this up in relation to rational numbers.

Answer 80

there should be an equal sign somewhere there

Answer 81

well,Syou are right