Kishan Patel	Hw6	10/3/21

1) The fifth postulate cannot be proven from the others as the first describes a line is defined by creating a line with 2 points, that straight lines are continuous, circles are defined by a distance from the center, and all right angles are equal to one another. These cannot define or prove the parallel axiom as none describe two continuous lines with angles non equal angles compared to a third line intersecting them will eventually meet at one point and if they have the same angle, they will never meet.

2) Godel's proof demonstrates that our reasoning is incomplete as there are proofs with no way of proving they are true, he does this by making paradoxical verbal statements that create an infinite loop to show our logic is incomplete.

3)Dr. Z's theory is to stop thinking about infinite possibilities/solutions as they only hinder us in explaining what can be explained, such as the infinite loop verbal paradox as it is pointless to dwell on.

3)
i)Finite loop as if we assume that B lies, then what B says is a lie that proves what A said, thus finite and true

ii) This is false as if A says B is true, then what A says is false which reverses what either say and continues infinitely

iii) False as this keeps flipping over and over on who is saying the truth or the lie

iv) This is true, as there is no infinite loop as A and C are truthfull and B D are liers.