Discrete MathLogic problem Carefully formulate the negation

Discrete Math/Logic problem

Carefully formulate the negation of the following statement. Then prove the statement by contradiction.

             There is no greatest even integer.

Solution

Negation statement : \"There exists a maximum value for an even integer\".

Let us take any even integer x. Let it be the maximum value.

Now If we see this, x+2 is also an even integer and x+2 > x. In that case x+2 becomes the maximum even integer now.

Again, (x+2) +2 is an even integer. And, ((x+2)+2) > (x+2). which makes (x+4) a greater even integer.

So, we can say our assumption is wrong.

Hence, we can say that there exists no greatest even integer. Hence, proved.