Question

Give examples of hypothesis and axioms....

Answer 1

Axiom- An axiom (or postulate) is a starting point of reasoning.In layman's language it is a statement universally accepted as true.

In mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms".

Logical axioms are usually statements that are taken to be true within the system of logic they define (e.g., (A and B) implies A), while non-logical axioms (e.g., a + b = b + a) are actually defining properties for the domain of a specific mathematical theory (such as arithmetic).

When used in the latter sense, "axiom," "postulate", and "assumption" may be used interchangeably.

for e.g.- "It is possible to extend a line segment continuously in both directions." another example is- "It is true that all right angles are equal to one another".

Conjecture-It is a conclusion  which appears to be correct based on incomplete information, but for which no proof has been found.

Such as Riemann hypothesis which states that that the non-trivial zeros of the Riemann zeta function all have real part 1/2.

But when a conjecture has been proven, it is no longer a conjecture but a "theorem". Many important theorems were once conjectures.