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#1 Re: Help Me ! » The formal definitions of the functions » 2012-01-21 08:14:26
Good point. But the thing is I am not sure how to calculate 14/5 without a calculator.
#2 Re: Help Me ! » The formal definitions of the functions » 2012-01-21 05:42:43
Oh I understand that concept. but when it comes with decimal numbers. It would take too long to find out the answer.
#3 Re: Help Me ! » The formal definitions of the functions » 2012-01-21 05:09:03
Hi StarShine;
You do not need a calculator or an unlimited amount of time. It is easy to solve linear equations of the type
5 x - 1 = 13 by a two step process.
Okay I will have a look at linear equations.
#4 Re: Help Me ! » The formal definitions of the functions » 2012-01-21 05:03:02
Ohhhhh boy. How am I gonna find that out. That will probably take forever without a calculator. Is there a quicker method? Or a link from Maths is fun website?
#5 Re: Help Me ! » The formal definitions of the functions » 2012-01-21 04:36:28
Ohh sorry. I meant 5*x where x is any number. In post 17, you seem to have divided 14 by 5 to reach 13.
Edit: Does that mean 5*2.8 = 14 -1 = 13 
#6 Re: Help Me ! » The formal definitions of the functions » 2012-01-21 03:48:11
Whaa.. shouldn't 5x be 5*n and then subtract by one?
#7 Re: Help Me ! » The formal definitions of the functions » 2012-01-21 02:38:38
Yes you are right. But, what if it was 5x-1 in Real numbers to Real numbers? It's injective and surjective, but how can you get 13 and 2 in this example to prove surjection?
#8 Re: Help Me ! » The formal definitions of the functions » 2012-01-21 02:10:42
Hi guys, I'm back. I have a quick question. Say, x^2+1 in integer to integer. I was wondering how is this not surjective? Is it because the codomain contains all numbers ...-7,-6,-5,-4....0....1,2,3,4,5..... and 'x^2+1' must hit all numbers in the codomain?
In surjection, does everything from the domain go to every element in the codomain too?
#9 Re: Help Me ! » This question doesn't make sense... (Relations...) » 2012-01-17 13:05:22
hi
i assume you mean the you are using 'is at least as clever as' as a relation.
look at it this way:
if you say 'John is at least as clever as Ann' it means the same as if you said 'John is as clever as Ann or cleverer than her'.so it's a little like the relation ≥. if you say 5≥3 then it's the same as saying 5>3 or 5=3.
but,you can also say 3≥3,because you need either 3>3 or 3=3.
similarly, if you say 'John is at least as clever as John' we could say this differently as 'John is as clever as John or is cleverer than John'.we know that John can't be cleverer than himself,but he is as clever as himself,and since one condition is satisfied,the statement is true.so John is at least as clever as John (assuming this is the same John)
Oh yeaa! I like what you said " 'John is at least as clever as Ann' it means the same as if you said 'John is as clever as Ann or cleverer than her'. " That clears things up.
But... here's is what I find awkward. Example, 'is a brother of' That's only Transitive. The funny thing is why is this not symmetric? If Bill is a brother of Steve. Then Steve is a brother of Bill. Or would you have to consider if Bill has a sister?
#10 Help Me ! » This question doesn't make sense... (Relations...) » 2012-01-17 04:21:19
- StarShine
- Replies: 3
Hi guys, I find this confusing. Here's the question: 'is at least as clever as'. The answer is Reflexive and Transitive, but not Symmetric. What I don't understand is how is it Reflexive? You can't be at least as clever as yourself. 
#11 Re: Help Me ! » The formal definitions of the functions » 2012-01-15 13:41:01
Ahh... I think I got this. I kinda rushed when I commented back before. Going to do a lot of these practice questions!
#12 Re: Help Me ! » The formal definitions of the functions » 2012-01-13 14:20:32
Hi StarShine;
Surjective means every B has at least one matching A ( look at the top diagrams on those pages ). The reals called R have negative numbers too. So when f(n) = n^2 how can you get -1 for instance. You can not. Nothing in R when squared will give you -1 so that function is not surjective.
You are right! 
It would be the same if it was integers. f(n) = n^2 would prove it's injective only, like Real Numbers. Same with positive integers too
#13 Re: Help Me ! » The formal definitions of the functions » 2012-01-12 15:40:40
Okay. I think I'm getting there and understanding this 
. I have one more simple quick question, if a function was real numbers to real numbers (not related to our previous examples above), would you use decimals to prove surjectivity??
#14 Re: Help Me ! » The formal definitions of the functions » 2012-01-12 02:46:15
Hi StarShine;
I am not following you there. If it was Q ( rationals ) we were speaking of then that would not be injective or surjective.
Rationals like 4 / 9 would be mapped by 2 rationals ( 2 / 3 ), -( 2 / 3 ) so it is not injective. Some members of the set Q would have no mapping like 17 / 19 for instance. What member of Q could you square to get that?
hmm.. this is tricky. I can't think of a member that goes into 17/19 :S Perhaps squaring decimals??? Ughh... fractions are the worst.
#15 Re: Help Me ! » The formal definitions of the functions » 2012-01-11 10:12:46
Hi StarShine;
That would be injective and not surjective, am I correct??
If you are talking about f(x) = x^2 in N then yes it is injective but not surjective. There is no f(x) that yields 3 for instance.
oh right!
if it was a rational number, would you just consider whole numbers or think about decimals and fractions too?
#16 Help Me ! » The formal definitions of the functions » 2012-01-11 08:00:30
- StarShine
- Replies: 30
Hello!
I was on a Maths is Fun website and looked up injective, surjective and bijective. I absolutely understand this as a functional diagram. However, I am stuck on the formal definitions.
Here is what I taken out from the website: "A function f is injective if and only if whenever f(x) = f(y), x = y." - Ok, I got that. I looked at an example of it...
"Example: f(x) = x^2 from the set of real numbers R to R is not an injective function because of this kind of thing:
f(2) = 4 and
f(-2) = 4
This is against the definition f(x) = f(y), x = y, because f(2) = f(-2) but 2 ≠ -2 "
Now, i understand that because the domain containing 2 and -2 both go to 4 in the codomain. On the other hand, what if they were natural numbers? That would be injective and not surjective, am I correct?? Because say you have f(2) = f(3), both go to seperate directions in the codomain, but uncertain if that meets the definition "f(x) = f(y), x = y".
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