Turn on thread page Beta
    • Thread Starter
    Offline

    12
    ReputationRep:
    little unsure
    Offline

    11
    ReputationRep:
    (Original post by Trackstar)
    little unsure
    Well, 1 can map to any of 1..n, 2 can map to any of 1..n, 3 can map to ...

    It's a problem in combinatorics.
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by atsruser)
    Well, 1 can map to any of 1..n, 2 can map to any of 1..n, 3 can map to ...

    It's a problem in combinatorics.
    yes, i thought n^2 but apparently its n^n
    Offline

    11
    ReputationRep:
    (Original post by Trackstar)
    yes, i thought n^2 but apparently its n^n
    Each choice of mapping for 1,2, .., n is independent of the others. So if there are n for each, how many in total?

    Maybe consider a more general but also more specific example: how many maps are there from {1, 2} to {1, 2, 3}? We can map 1 to 1,2, or 3, and we can map 2 to 1,2, or 3 independently, so in total ...
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by atsruser)
    Each choice of mapping for 1,2, .., n is independent of the others. So if there are n for each, how many in total?

    Maybe consider a more general but also more specific example: how many maps are there from {1, 2} to {1, 2, 3}? We can map 1 to 1,2, or 3, and we can map 2 to 1,2, or 3 independently, so in total ...
    yeah, so what i cant get my head around is that because 1 maps to all of 1,2,..n and so does 2, 3 etc and this happens n times it would just be n*n n^2
    Offline

    11
    ReputationRep:
    (Original post by Trackstar)
    and this happens n times it would just be n*n n^2
    This isn't right. If I want to count the mappings from {1,2,3} to {1,2,3,4}, then there are 4 choices for 1, 4 choices for 2, 4 choices for 3. Each of these can be made independently. So how many in total are there? Think of making a tree of combinations - how many branches would you need at each stage?
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by atsruser)
    This isn't right. If I want to count the mappings from {1,2,3} to {1,2,3,4}, then there are 4 choices for 1, 4 choices for 2, 4 choices for 3. Each of these can be made independently. So how many in total are there? Think of making a tree of combinations - how many branches would you need at each stage?
    okay, are you saying that you then have to include all the different combinations in which {1,2,3} can map to {1,2,3,4} say 1-2, 2-3, 3-4 is one, 1-4, 2-3, 3-1 is another.
    Offline

    11
    ReputationRep:
    (Original post by Trackstar)
    okay, are you saying that you then have to include all the different combinations in which {1,2,3} can map to {1,2,3,4} say 1-2, 2-3, 3-4 is one, 1-4, 2-3, 3-1 is another.
    Actually forget the tree of combinations idea - I don't think that's a good way to represent things. However, yes, you are thinking along the right lines. Have you heard of the fundamental counting principle in combinatorics? If not, you should google it.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: October 6, 2017
Poll
Do you think parents should charge rent?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.