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Do you know what a function is?

yes

you are given variables and replaced by numbers for short

no. please explain

ok. so the first is injective?

correct

the second one is not because 1 and 2 both get sent to a

ok

in any function, every x maps to at most one y in the range

read this http://www.math.ucla.edu/~tao/java/MultipleChoice/functions.txt

ok

injective

why?

because each maps differently and are all exhausted in the left

gil
no two x values map to the same y value.
agreed?

yes

no

why ot?

remember that surjective just means that the entire codomain (the circle on the right) gets used up

because no single element of X mspd to two elements of Y

read my last comment

what you just said is true of all functions

oh ok

ok so when it is both surjective and injective we call it a bijection.

ok

Now think about why these things are saying what we talked about above.

ok buy i do not understand this

buy ?

but

ok

does that make sense?

yes thanks

when will you be online again sir?

most likely