Thm 11.1.2 (the pigeonhole principle):
Suppose that f:X( Y is a function between non-empty finite sets such
that |X| > |Y|. Then f is not an injection, i.e. there exist distinct
elements x1 and x2 E (epsilon) X such that f(x1) = f(x2).
Mathematics Homework Solutions
#54872
Proof problem
Need help in determining the following proof.
(See attached file for full problem description)
---
Thm 11.1.2 (the pigeonhole principle):
Suppose that f:X Y is a function between non-empty finite sets such that |X| > |Y|. Then f is not an injection, i.e. there exist distinct elements x1 and x2 E (epsilon) X such that f(x1) = f(x2).
---
This solution is comprised of a detailed explanation to prove the problem.
What is this?
By OTA - Overall OTA Rating
Yupei Xiong, PhD - 4.8/5
Purchase Cost Now
$2.19 CAD (was ~$7.98)
Included in Download
- Plain text response
Why you can trust BrainMass.com
- Your Information is Secure
- Best Online Academic Help Service
- Students find real academic Success
- Math Proof - College level proof before real analysis. Please give formal proof. Please explain each step of your solution. If you have any suggestion or question to me, please let me know. Thank you. Prove ...
- Criticism of a proof - Criticize the following proof...(see attachment)
- Differentiation Proof - By following the proof that d/dx e^x , show that for f(x) = a^x, d/dx a^x = f'(o)a^x.
- Partial Induction Proof of Cauchy's Integral Formula - see attached file...it is a full induction proof of Cauchy Integral Formula, with the base case step missing. All I have to do is show that it holds for "n=1", using the rest of the proof as an examp ...
- Analyticity Proof - Suppose that f: C->C and that f is analytic at a point z0 element of C. Prove that there exists a real number r>0 such that, the nth derivative of z0=[n!/(2 pi r^n)]x[int(e^(-niy)f(z0+re^(iy)) from 0 ...
