Mathematical statement whose truth has been proved is called :

Question

Accepted Answer

A mathematical statement whose truth has been proved is called a "Theorem." Let's delve into why Option 1 is the correct choice and why the other options are not suitable.

1. **Theorem (Option 1):** 
   - A theorem is a statement that has been proven to be true through a logical sequence of arguments based on previously established statements, such as axioms, postulates, or other theorems. The process of proving a theorem involves rigorous logical reasoning and is a fundamental aspect of mathematical practice. Once a theorem is proven, it is universally accepted as true within the context of the given axiomatic system. This is why the term "theorem" is specifically used for statements that have been conclusively demonstrated to be true.

2. **Axiom (Option 2):**
   - An axiom is a statement that is accepted as true without proof. Axioms serve as the foundational building blocks for a mathematical system. They are assumed to be self-evident and are used to derive theorems and other mathematical truths. Since axioms are not proven but assumed, they do not fit the description of a statement whose truth has been proved.

3. **Conjecture (Option 3):**
   - A conjecture is a statement that is proposed to be true based on observations or intuition but has not yet been proven. Conjectures are often the starting point for mathematical exploration and research. Until a conjecture is proven, it remains an unverified hypothesis. Therefore, a conjecture does not meet the criteria of a statement whose truth has been established through proof.

4. **Postulates (Option 4):**
   - Postulates are similar to axioms in that they are assumed to be true without proof. They are specific assumptions used to build a particular mathematical theory. Like axioms, postulates are foundational and are not proven, so they do not qualify as statements whose truth has been demonstrated.

In summary, the term "theorem" is uniquely reserved for mathematical statements that have been rigorously proven to be true, distinguishing it from axioms, conjectures, and postulates, which do not meet this criterion. Therefore, Option 1, "Theorem," is the correct answer.