Rational & Irrational Number For a - b

[nycmathguy]

Set 1.1

Give an example of irrational numbers a
and b such that the indicated expression is (a) rational and (b) irrational.

Note: The above instructions are given for problems 56, 57, and 58. David Cohen did not include a subtraction problem for this set of instructions.

I made up the problem a - b.

Let me guess. I must subtract b from a to yield a rational number and also an irrational number.

Yes?

 

[MathLover1]

Let z be any irrational number.
let a = 1+z and b = 1-z.
a+b = 1 + z + 1 - z = 2 (rational)

 

[nycmathguy]

Let z be any irrational number.
let a = 1+z and b = 1-z.
a+b = 1 + z + 1 - z = 2 (rational)

I now have to do the same to show that a - b is irrational. Yes?

Can you check my thread zero^(zero) posted on July 20 here?