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. */
}