" Define an irrational number."

Define the irrational numbers. Give examples.

Every irrational number

The sum; Difference;poduct and quotient of two irrational numbers need not be an irrational number.

Give an example of each, of two irrational numbers whose: (i) difference is a rational number. (ii) difference is an irrational number. (iii) sum is a rational number. (iv) sum is an irrational number. (v) product is a rational number. (vi) product is an irrational number. (vii) quotient is a rational number. (viii) quotient is an irrational number.

Prove the following by contradiction : "The sum of a rational and irrational number is an irrational number ."

Give an example of each,of two irrational numbers whose: difference is a rational number.difference is an irrational number. sum is a rational number.sum is an irrational number.product is a rational number.product is an irrrational number.quotient is a rational number.quotient is an irrational number.

If f: [0,1] to R is defined by the rule f (x) = {{:(x, "if x is a rational number"),(1 -x, "if x is an irrational number"):} then :

Prove that the sum of or the difference between, a rational number alpha and an irrational number beta is an irrational number.

Negation of an irrational number is an irrational number.

Give an example of non-algebraic irrational number ? If irrational what type of irrational ( pi - n) is an irrational number.