A form of

proof in which the

premise is proved

true by

assuming that it's true. Proof by

Assertion is actually a

logical fallacy, or a method in an

unproof. It is

an extreme case of

Begging the Question.

An example: "It's true because it's true".

To prove the use of Proof by Assertion, prove that the conclusion is one of the premises.

This should not be

confused with the use of assertions in proofs, particularly proofs of

algorithms. In these cases, the assertion is used to introduce as a

premise what has been proven

up to this point. For example, a proof of a simple sorting algorithm gone

a little overboard with assertions:

void sort(int [a], int length){
int i, k;
for(i=0; i<length; i++){
/* ASSERT: a[0..i] is sorted */
/* ASSERT: all elements in a[0..i] are <= all elements
in a[i..length] */
k=indexOfSmallest(a, i, length);
/* ASSERT: k has the index of the smallest element in the
unsorted portion of a */
swap(a, i, k);
/* ASSERT: a[0..i] <= a[i] <= a[i+1..length] */
/* Because a[0..i] is sorted and a[0..i] <= a[i],
a[0..i+1] is sorted */
}
/* because i==length and a[0..i] is sorted, a is sorted. */
}