Functions

[Yendall]

I think i'm having difficulty, not with the math itself, but the interpretation of the questions. Here is the question:

Let B = {0,1}. If f:B --> B is defined by f(n) = 1 - n^2 then which one or more of the following is/are true? (Note that n^2 here means "n squared".)
I interpret this as a table:



So this would be a one-to-one function and an onto function.


This is where i don't understand, in questions like these:

Let B = {0,1}. If f:B --> Q is defined by f(n) = 1 - n^2 then which one or more of the following is/are true? (Note that n^2 here means "n squared".)

Do I follow the same method? When B is mapping to Q, what order are the numbers presented in inside Q? Q is the set of rational numbers, so how does this work when B = {0,1} ?

Thanks for any help

[kamil9876]

It's hard to help you out when you havn't written down the question completely. The question "which one or more of the following are true?" probably suggests that there are certain statements that follow, which you havn't provided.

what order are the numbers presented in inside Q?

What does "order" and "presented in inside" mean and why should it have anything to do with anything?

Q is the set of rational numbers, so how does this work when B = {0,1} ?

Well via the identification and so this is a well defined function, I don't see the issue?

[abeybaby]

maybe thats why he goes to assumption college

[Yendall]

maybe thats why he goes to assumption college

That was just completely unnecessary..... unless that was a joke.

[deleted]

maybe thats why he goes to assumption college

went* he graduated already

[Yendall]

It's hard to help you out when you havn't written down the question completely. The question "which one or more of the following are true?" probably suggests that there are certain statements that follow, which you havn't provided.

Well via the identification and so this is a well defined function, I don't see the issue?

Sorry, the possiblities are:

• One-To-One Function
• Onto Function
• Not a function
• A function, but not One-To-One or Onto

"What does "order" and "presented in inside" mean and why should it have anything to do with anything?"

I worded that terribly, don't worry.

[abeybaby]

That was just completely unnecessary..... unless that was a joke.

yes it was a joke.. sorry if you got offended

edit: ohhhh sorry, i see, no i didnt mean it as an attack on the school, itvwas just a play on words cos we had to assume what the options were. sorry again

[kamil9876]

Sorry, the possiblities are:

• One-To-One Function
• Onto Function
• Not a function
• A function, but not One-To-One or Onto

So the map given by is a one-to-one function but is not onto since  but there is no such that .

Notice that the previous function that sends every element to itself is indeed onto. Hence the co-domain is important (and so even though they behave in the same way)

[Yendall]

Thank you! i spent a while on Sunday night figuring all this stuff out, now I can do it without thinking haha