Can You Solve This Onto, But Not One-to-One Function Challenge?

  • Context: Undergrad 
  • Thread starter Thread starter Jrb599
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Discussion Overview

The discussion revolves around finding a function from the natural numbers to the natural numbers that is onto but not one-to-one. Participants explore various function definitions and attempt to identify suitable examples.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant requests suggestions for a function that is onto but not one-to-one.
  • Another participant suggests a function definition but notes it does not meet the criteria.
  • There is a proposal of a function where f(1) = 2 and f(x) = x for x > 1, which is later deemed not to work.
  • A different function is proposed: f(1) = 1, f(2) = 1, and f(n) = n - 1 for n > 2, with one participant affirming it meets the criteria.
  • Further suggestions include f(x) = 2x and the greatest integer function, but these are questioned or dismissed.
  • One participant expresses gratitude for the help received in finding a solution.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single function that satisfies the criteria, as multiple proposals are made and some are challenged or rejected.

Contextual Notes

Some proposed functions are not fully explored or validated, and there are unresolved questions regarding the definitions and properties of the functions discussed.

Who May Find This Useful

Individuals interested in mathematical functions, particularly in the context of properties like being onto and not one-to-one, may find this discussion relevant.

Jrb599
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[SOLVED] Onto, but not one-to-one

I need a function

f: N -> N such that f is onto, but not one-to-one, and I can't think of one to save my life, any suggestions?
 
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f({a,b}) = {x}.

Sorry, you posted N to N...
 
what does {x} stand for?
 
f(1) = 2
f(x) = x for x > 1.

Doesn't work.

Hmm...
 
Last edited:
what about

f(1)=1
f(2)=1
f(n) = n-1 for n>2
 
I think you have just found one.
 
k, well your original post helped me, so thank you!
 
what about f(x) = 2x? no...

or greatest integer not greatER THan x/2, +1?

or f(x) = x-1, for x >1 and let's see f(!) = ?

how long did you think about this?
 

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