/sci/ - Science & Math

[Anonymous No.9995903]

>proposition
>corollary
>lemma
>theorem
>postulate
>conjecture
>claim

Will someone autistic explain these to me?

And why did we let the old fart mathematicians create an orgy of confusing language? Us new mathematicians need to clean this up. Any suggestions for a new mathematical language?

[Anonymous No.9995907]

>>9995903
> i have to learn the definitions of 7 words :'-(
> i'm studying math, which means memorizing hundreds of definitions

[Anonymous No.9995911]

>>9995907
>memorizing

I don't speak brainlet, what is memorization? I deduce all definitions empircally.

[sdleif lla ni seog egas No.9995930]

>proposition
Simply a noteworthy fact, usually accompanied by a short proof.

>corollary
A direct consequence of a theorem.

>lemma
A lesser statement that will be used to prove a more important one, the latter of which is usually the focus of a paper or textbook chapter.

>theorem
A statement proven true.

>postulate
An axiom: something regarded to be true without proof. The name "postulate" is used in Euclid's Elements and I pretty much haven't seen it outside of this context.

>conjecture
>claim
Both denote a statement whose truth value we do not know yet. A mathematician conjectures statements to be true and then later goes on to prove or disprove it.

Brainlet.

[Anonymous No.9995939]

>>9995903
>>proposition
Usually synonymous with theorem (see below), especially in the sense of Euclid.
>>corollary
Something that goes along with a theorem; a statement that is similar to but that has a distinct proof from another related statement.
>>lemma
A miniature theorem; usually stated to work as a part of a larger proof/statement.
>>theorem
A statement that has been proven a priori given the rules and axioms of the maths at hand. Theorems are absolutely true statements that follow necessarily from certain initial assumptions and logic.
>>postulate
An axiom, but especially of the physical sort. The rigorous theory of relativity begins with some postulates (like c is constant, all acceleration is equivalent, and others) that have no proof, but instead are taken for granted.
>>conjecture
A scientist might call it a hypothesis, but a conjecture is a statement that has no known truth.Conjectures are not known to be true or false in the absolute sense.
>>claim
Literally, a claim.

[Anonymous No.9995944]

>>9995911
>I deduce all definitions empircally.
you're like the math equivalent of pic related. You do not "deduce" definitions.