Axioms and Postulate difference:

The terms "postulates" and "axioms" are often used interchangeably in mathematics, especially in the context of Euclidean geometry, but they have subtle differences based on their historical usage and context in various branches of mathematics. Here's a simple analogy to explain the difference, followed by a more detailed explanation.

Simple Analogy Think of building a house:

Axioms are like the basic laws of construction that apply everywhere, such as gravity and the need for a stable foundation. These rules are so fundamental and universally accepted that everyone building anything, anywhere, agrees on them. Postulates are like the specific rules you decide to follow for your house, such as choosing to build it with a certain type of material or deciding that all the rooms will have natural light. These rules are specific to the project you're working on and are chosen because they suit what you want to achieve.

After Euclid stated his postulates and axioms, he used them to prove other results. Then using these results, he proved some more results by applying deductive reasoning. The statements that were proved are called propositions or theorems. Euclid deduced 465 propositions in a logical chain using his axioms, postulates, definitions and theorems proved earlier in the chain.