The negation of statement p is not p For example for the sta

The negation of statement p is \"not p.\" For example, for the statement \"The number 9 is odd,\" its negation is \"the number 9 is not odd.\" Another example, for the statement \"A can buy anything,\" its negation is \"there is at least one thing such that A cannot buy it.\" Consider the following statement: given a sequence {a_n}, there exists a positive number M, such that |a_n| M for any n. What is the negation of the above statement ?

Solution

Negation of given statement:

Given a sequence {a_n}, there exists a +ve number M, such that |a_n| > M for any n.