Thursday
December 12, 2013

Homework Help: discrete math

Posted by thisha on Thursday, September 28, 2006 at 6:10pm.

1)prove that if x is rational and x not equal to 0, then 1/x is rational.

2) prove that there is a positive integers that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive?

For 1) use the definition of a non-zero rational number.
Defn: A non-zero rational is any number that can be expressed as p/q where p and q are non-zero integers.
If p/q is rational, then how about q/p?

For 2) you should be able to supply both a constructive and non-consructive proof.
Since the sum of any finite set of integers is an integer, there exists an integer for the sum of the first +n integers.
There is a formula for this, but I'll let you work on this.

Related Questions

discrete math - Let A= {for all m that's an element of the integers | m=3k+7 for...
Discrete Math - If n is a positive integer and n > 1,prove that (n) + (n-1) ...
discrete math - If a and b are positive integers, prove that; ab = gcd(a,b)*lcm(...
DISCRETE MATHS - Prove that for every set S, Ø \subseteq( S. i need to Use ...
Discrete Math - Prove that if a and b are integers with a not equal to zero and ...
Discrete Math - If n is a positive integer and n > 1, prove that (n over 2...
discrete math - 5= (1+4) (1+4)^n= 1^n + 2*1*4 + ...+4^n which is 1 mod 4 Prove ...
Discrete Math - 1. Assume that n is a positive integer. Use the proof by ...
DISCRETE MATHS - Prove that if n is an odd positive integer, then 1 ≡ n2 (...
Discrete Mathematics - Let m,n,z belong to N such that m and n divide z and gcd...

Search
Members