73.1k views
0 votes
Is a postulate another name for a conjecture we believe to be true?

a) Yes
b) No
c) Sometimes
d) It depends on the context

User Astuetz
by
7.9k points

1 Answer

1 vote

Final answer:

A postulate is an assumed true statement in mathematics, while a conjecture is a yet-to-be-proven hypothesis. They are not the same; a postulate is a foundational element, unlike a conjecture which is an informed guess. 'Suggestion' is the term closest related to 'hypothesis'.

Step-by-step explanation:

The student has asked whether a postulate is another name for a conjecture that we believe to be true. The answer is No, a postulate and a conjecture represent different concepts in mathematics. A postulate, or axiom, is a statement that is assumed true without proof and serves as a starting point for further reasoning and arguments. It's fundamental to building the framework of a mathematical system. On the other hand, a conjecture is an informed guess or hypothesis that is based on observations but has not yet been proved or disproved.

For example, Euclid's postulates form the basis of Euclidean geometry and are accepted without proof. Conversely, the Goldbach Conjecture, which suggests that every even integer greater than two is the sum of two primes, is still a conjecture because it has not been either proved or disproved despite being widely believed and accepted by many.

To the question related to 'hypothesis', the closest term from the given options is suggestion. A hypothesis is an educated guess or proposal that is subject to verification by further investigation or experimentation.

User Galactus
by
7.6k points