No. Conjectures are "good" guesses.
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Usually not. If you do use conjectures, you should make it quite clear that the proof stands and falls with the truth of the conjecture. That is, if the conjecture happens to be false, then the proof of your statement turns out to be invalid.
Conjectures and statements differ primarily in their nature and certainty. A statement is a declarative sentence that can be classified as true or false, while a conjecture is a proposition that is believed to be true based on observations or patterns but has not yet been proven. Essentially, all conjectures are statements, but not all statements are conjectures; some may be established facts. Conjectures often serve as hypotheses in mathematical and scientific contexts that require further investigation or proof.
The corollaries types of statement is what is used to explain the steps of a proof.
The corollaries types of statement is what is used to explain the steps of a proof.
In geometry, deductive rules can be used to prove conjectures.
prove conjectures
Counterexamples are used to test the validity of conjectures by providing a specific instance where a conjecture fails. If a counterexample is found, it refutes the conjecture, demonstrating that it is invalid. Conversely, if no counterexamples can be found despite thorough testing, it supports the conjecture's validity, although this does not prove it universally true. Thus, while counterexamples are critical for refutation, their absence strengthens the case for a conjecture, though further proof may still be needed for confirmation.
Some words that rhyme with "lectures" are textures, conjectures, and ruptures.
surmises
inductive
hypotheses or more generally conjectures should be capable of being refuted see: Karl Popper - Conjectures and Refutations