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.

## Answer this Question

## Related Questions

- discrete math - Let f:ℤ+ → ℤ+ be the function defined by: for...
- discrete math - Let A= {for all m that's an element of the integers | m=3k+7 for...
- math - Find the sum of all positive integers m such that 2^m can be expressed as...
- Math - I just wanted to check my answers with anyone willing to take the time. ...
- discrete math - If a and b are positive integers, prove that; ab = gcd(a,b)*lcm(...
- math - Let f:ℤ+ → ℤ+ be the function defined by: for each x &#...
- Math - Pick 2 consecutive, positive integers and call them a and b. Prove that a...
- math help please - Let f:ℤ+ → ℤ+ be the function defined by: ...
- math - Prove that a number 10^(3n+1) , where n is a positive integer, cannot be ...
- Maths - Prove that a number 10^(3n+1) , where n is a positive integer, cannot be...

More Related Questions