Question

Which of the following sets represents a function?



a.{(3, 5), (-1, 7), (3, 9)}

b.{(1, 2), (3, 2), (5, 7)}

c.{(1, 2), (1, 4), (1, 6)}

Answer 1

The same \(x\) cannot have more than one \(y\) value for a relation to be a function

Answer 2

that means \(x\) values cannot repeat

Answer 3

So for example, the first one cannot be a function because it has 2 y values when x is 3.
(3,5) and (3,9)

Answer 4

technically they can \(\{(1,2),(1,2),(3,4)\}=\{(1,2),(2,3)\}\)

Answer 5

that last one should be 3,4

Answer 6

{1, 1, 1} = {1}
so these sets are equivalent right ?

Answer 7

yes

Answer 8

but at this level they prob wont try and trick you like that...

Answer 9

so they cannot repeat is technically also a correct phrase ?

Answer 10

\(\{(1,2),(1,2),(3,4)\}=\{(1,2),(3,4)\}

\)

Answer 11

they are repeating and they are both a function

Answer 12

are you really sure you want to have repeating elements in a set ?

Answer 13

you don't want to, but these are the same. So you could ...

Answer 14

OK

Answer 15

then some teachers might use it to trick :P

Answer 16

But in this case we can exclude C...?

Answer 17

its silly I know... Just two people said it, so I wanted to be clear. And the OP and I just discussed the fact that we don't want to list elements in a set twice if we want to be clear

Answer 18

for sure

Answer 19

we can list elements of the cross product twice

Answer 20

Maybe we should delete this as not to confuse the user?

Answer 21

{1, 2, 3} x {1, 2, 3}

cross product will have distinct elements

Answer 22

I am in Canada in getting "Coffee" and I might be a little to talkative @iambatman

Answer 23

Haha, fine with me :)

Answer 24

I meant we can have (1,2)(1,2) these are the same element in the cross product

we cant have (1,2) (1,2) there are not the same in the cross product, but do "repeat" in a sense.

Answer 25

errr we cant have (1,2) (1,3) ....

Answer 26

all I am saying is what you guys mean is that we cant have repeated x coordinates in different elements

Answer 27

the elements are ordered pairs...

Answer 28

yeah i was kindof torn between being precice and helping the user

anyways this makes me think of the precice definition of cardinality of a set as we have {1} = {1, 1, 1}

Answer 29

both sets have 1 element

Answer 30

there is only one bijection from {1,1,1} to {1}

Answer 31

I see you're particular about pattern earlier

Answer 32

Gotcha :)

Answer 33

err since there is a bijection.....

Answer 34

1 -> 1

Answer 35

TO be very technical

since there is a bijection between \(\{1\},\{1,1,\},\) and \( \{\emptyset\}\)
the have the same cardinality which is 1

Answer 36

the actual definition of a set doesn't bother about pattern i guess
it is based on existence of elements in a set

also i remember from analysis class that we take sets for granted and definition is not really that precice

Answer 37

Set theory.

So easy it does not have a definition.

Answer 38

lol

Answer 39

someone said that to me once....

Answer 40

the more I study set theory the more I realize that most everything is based off of an assumption that I am starting to have some problems with.

Answer 41

and a definition that is not precise...

Answer 42

lol