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18 lines
No EOL
1.2 KiB
Markdown
Executable file
# Mathematics
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Welcome to the mathematics page. Some special mathematical environments that will be used in this section are listed and explained below.
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* *Definitions* : a precise and unambiguous description of the meaning of a mathematical term. It char-
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acterizes the meaning of a word by giving all the properties and only those properties that must be
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true.
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* *Theorems* : a mathematical statement that is proved to be true using rigorous mathematical reasoning. In
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a mathematical text, the term theorem is often reserved for the most important results.
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* *Propositions* : an often interesting result, but generally less important than a theorem.
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* *Lemmas* : a minor result whose purpose is to help in proving a theorem. It is a stepping stone on the path
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to proving a theorem.
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* *Corollaries* : a result in which the (usually short) proof relies heavily on a given theorem (we often say
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that this is a corollary to Theorem A).
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* *Proofs* : a convincing argument that a certain mathematical statement is necessarily true. A proof
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generally uses deductive reasoning and logic but also contains some amount of ordinary language.
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* *Examples* : examples help to understand the meaning of a definition, or the impact of a result.
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* *Algorithms* : recipes to do calculations. |