A conjecture is a proposition or conclusion based on incomplete information, which is believed to be true but has not yet been proven. It plays a crucial role in the development of mathematical theories and scientific hypotheses, often serving as a starting point for further investigation and proof.

Conjecture

conjecture

A proposition is a declarative statement that can be either true or false, serving as the foundational building block in logic and philosophy. It is crucial in constructing arguments, proofs, and theories, providing a basis for reasoning and communication of ideas.

proposition

A conclusion is the final part of a discourse or text that summarizes the main points and provides closure. It often reinforces the thesis or main argument, leaving the audience with a clear understanding or call to action.

conclusion

Incomplete information refers to a scenario where all parties in a decision-making process do not have full knowledge about the relevant factors or the other parties' intentions, preferences, or actions. This can lead to strategic behavior and inefficiencies in markets, negotiations, and games, as agents must make decisions based on limited or asymmetric information.

incomplete information

Mathematical theories are frameworks of ideas and principles that address particular sets of problems or questions within mathematics, providing rigorously derived results using logical reasoning. They serve as the foundational structures from which mathematicians prove theorems and solve complex problems, often leading to new discoveries and applications across various fields.

mathematical theories

scientific hypotheses

A starting point is the crucial initial step or position from which progress or development begins. Understanding this concept provides clarity, focus, and direction for any task or journey, ensuring stable groundwork for achievement and growth.

starting point

further investigation

Proof is a logical argument that establishes the truth of a statement based on axioms, definitions, and previously established theorems. It is fundamental in mathematics and logic, ensuring that conclusions are derived with certainty from given premises.

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