Question

For which operations is the set -1,0,1 closed? Choose all answers that are correct
A: addition
B: division
C: multiplication
D: subtraction

Answer 1

You can select any number from that set and by adding, them if you get a number which is there in set too, you will say for Addition, the set is closed.. :)

Answer 2

\(1 + 1 = ??\)

Answer 3

@Passion567 first of all,do you know what is the meaning of closed interval ?

Answer 4

no

Answer 5

it means that when you apply any mathematical property on numbers,if the answer would come only and only -1,0,1 ,then we can say that the result(answer) is closed in the interval

Answer 6

understood? @Passion567

Answer 7

somewhat

Answer 8

so
for option A) if you add,then you will get :-
-1+0=-1
1+0=1
-1+1=0

Can we say that option A is closed in the set?

Answer 9

could you get that ? @Passion567

Answer 10

no i have no clue what this is i do homeschool and they dont teach us about it they just give us test and make us take them

Answer 11

@mayankdevnani you need to check it once again, If I will do \(1+1\), then result will not be in the given interval, sorry, but I am here in doubt.. :(

Answer 12

well, @Passion567 see the result from option A is closed because the results are as follows:--1,0,1 and this result is include in the set which is given in the question.

So,option A is correct

Answer 13

likewise,check all the other options

Answer 14

now @waterineyes you tried option D) subtraction
See :-
-1-(0)=-1---------->CLOSED
1-(0)=1------------->CLOSED
-1-(1)=-2------------>OPEN(NOT CLOSED)

Answer 15

hope you understand. @Passion567 @waterineyes

Answer 16

ok thank you

Answer 17

so option D is not our answer

Answer 18

so option D is not our answer :)

Answer 19

WELCOME :) @Passion567

Answer 20

In my knowledge, option A ie addition is not correct one.. :)

Answer 21

why ???

Answer 22

ok why

Answer 23

option A satisfies all the conditions

Answer 24

I mean can't we add 1 with 1 itself?

Answer 25

why ???? only +1 and -1 is given in the question ?

Answer 26

You can try one number only once

Answer 27

http://mathforum.org/library/drmath/view/52422.html

Answer 28

1 and 1 both are in the set.. :)

Answer 29

yeah...you are right !!!

Answer 30

but I am still in doubt.. :P

Answer 31

@Passion567 @waterineyes is right

We have to include all the numbers

Answer 32

no,i got it @waterineyes

Answer 33

Wait, I will give one other link which will contradict me and prove you are right, and answer is too given by jimthompson there.. :P

Answer 34

http://www.algebra.com/algebra/homework/Number-Line/Number-Line.faq.question.160073.html

Answer 35

So, now we are both equal.. Be happy.. :P

Answer 36

@ganeshie8

Answer 37

lolz.. @waterineyes

Answer 38

@ikram002p

Answer 39

Yeah, surely we need experts' advice here.. :) I have got rusty on set related things.. :)

Answer 40

:P

Answer 41

It seems like you have read it now somewhere and then you have come here.. :P

Answer 42

i get it !!!
Think @waterineyes
\[\large \bf [-1,0,1]\]

Answer 43

Okay, I am thinking.. @mayankdevnani

Answer 44

if we choose 1 from the set,now there are two numbers remaining i.e -1 and 0.
That's why,we can't add 1+1 ???

Answer 45

yes?? I am in doubt.. :)

Answer 46

you have to select two numbers from the set, why can't I choose one number twice?

Answer 47

for part A
1+1=2
for B
1/0 = :O
for D
-1-1=-2

so if i were u i would only chose C O.O

Answer 48

yippie, Ikram is on my side.. :P

Answer 49

lolzz

Answer 50

but JIMTHOMPSON

Answer 51

he is on my SIDE

Answer 52

:)

Answer 53

Sorry talk about online members.. :P

Answer 54

hmmm im on my side too ^_^

Answer 55

GREAT ^^^

Answer 56

That does not matter here.. :P

Answer 57

i would go with A, B, C
lets conduct a poll maybe :)

Answer 58

B also??

Answer 59

`poll`
Whow !!!!

Answer 60

Sorry, but you are alone here @ganeshie8 :P

Answer 61

@ganeshie8 you can't go with option B because 1/0=undefined which is open in the interval

Answer 62

One thing I am sure about, ganesh has proven that also as wrong.. I was sure about Division.. What man.!! :P

Answer 63

thats precicely the reason we can go with it, 1/0 is not defined in any of the number sets yet the real numbers are closed under division and multiplication right ?

Answer 64

since 1/0 is not defined, we don't bother about it when considering closure

Answer 65

ganesh R* is closed :) R itself nope

Answer 66

No ganesh.. :)

Answer 67

then il need updates :) whats R* ikram ?

Answer 68

R*=R-{0}

Answer 69

@ganeshie8 think that :-
the set is closed it means that only -1,0,1 (integral values) are considered.
1/0=undefined and UNDEFINED is not in this particular set !!!

Answer 70

please think over this

Answer 71

*UNDEFINED is not considered in this set

Answer 72

only under division R is not closed hmm
but this is also an axiom thingy :P
some books dont mention that so its ok sometimes to say R is closed on division

Answer 73

no,we can't say that UNDEFINED is closed because its UNDERSTOOD or apply common sense,how can we arrange UNDEFINED ??

Answer 74

@ikram002p

Answer 75

okay tjat makes sense, so real numbers are not closed under division because 1/0 is undefined ?

Answer 76

If i would say that :-
arrange planets in the market for market sale
Now can you arrange real planets for MARKET SALE

Answer 77

this guy failed me again
http://mathforum.org/library/drmath/view/61270.html

Answer 78

hehe yeah was gonna say about never heard of subtraction or division xD
but i thought explaining it like this more better :P

Answer 79

Ganeshie - Don't feel discouraged, that ''guy'' is a doctor for a reason. Hehe.

Answer 80

yeah i am still with him :) just trying to manage the strong opposition here haha!

Answer 81

i think :-
\[\large \bf ({- \infty,+ \infty})\]
i think @real numbers can be arranged in this set,

Answer 82

don't you think about that ? @ganeshie8 @ikram002p

Answer 83

well i like to be simple xD
i dont wanna show up hehe
so IMHO its only C , otherwise hmm i dont wanna comment :P

Answer 84

integers are closed under division makes sense because 1/3 is defined yet not an integer

however 1/0 itself is undefined, so real numbers are closed under division makes more sense to me..

Answer 85

but i believe u more @ikram002p so lets kick option B

Answer 86

yeah,,,option C would definitely satisfies.
option C is one of the answers

Answer 87

ganesh integer is not closed under division or multiplication this is what u trying to say right ?

Answer 88

integers are closed under multiplication right ?

Answer 89

nope

Answer 90

ugh, let me think

Answer 91

there is no such a^-1 in N for all a in N
such that
aa^-1=1 :O

Answer 92

@ikram002p and @ganeshie8 scroll up and see those comments from which the doubt has occur ?
and please be patient while you read all the comments and if you read all that comments,then please reply !!!

Answer 93

please TAKE YOUR TIME !!!

Answer 94

*while you are reading

Answer 95

how is multiplcation even related to inverse ?