数学中推论的英文简写

数学中推论的英文简写
In mathematics, a theorem is a statement that has been proven to be true based on logical deduction from previously established propositions or axioms. A theorem is a fundamental building block of mathematical knowledge that helps to establish the validity of mathematical arguments and provides a foundation for further study and exploration.
One common way to denote a theorem in mathematical writing is by using a numbering system. Theorems are typically numbered consecutively, and the numbering format may vary depending on the style guide or convention being followed. For example, a theorem may be denoted as Theorem 1.1 if it is the first theorem in Section 1 of a document. Subsequent theorems in the same section may be labeled Theorem 1.2, Theorem 1.3, and so on.
In addition to numbering, theorems are often given names or titles to provide a concise description of the statement or to honor the mathematician who first proved it. For example, we have the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Other famous theorems include the Bolzano-Weierstrass theorem, the Fundamental Theorem of Calculus, and Fermat's Last Theorem.
When referencing a theorem in mathematical writing, it is common to use their short names or numbers along with appropriate abbreviations. The abbreviation "Thm." is commonly used to refer to a theorem, followed by either the theorem number or name. For example, one might write "According to Thm. 1.1" or "By the
Pythagorean theorem" to refer to a specific theorem in a proof. This helps to clearly identify the source of the statement and allows readers to easily locate the theorem if they wish to verify it.
In addition to theorems, mathematics also relies heavily on lemmas, propositions, corollaries, and conjectures. These are all types of statements that play different roles in mathematical reasoning. Lemmas are auxiliary results that help in proving larger theorems. They are often used as intermediate steps or specialized cases of more general theorems. Propositions are statements that are not central to the main argument but provide additional information or support to theorems or lemmas. Corollaries are direct consequences or immediate extensions of theorems. Conjectures, on the other hand, are statements that are believed to be true but have not yet been proven. They serve as research problems and motivations for further investigation.
When addressing these different types of statements, similar abbreviations can be used. For instance, "Lem." can stand for lemma, "Prop." for proposition, "Cor." for corollary, and "Conj." for conjecture. These abbreviations can help to efficiently convey information and maintain clarity in mathematical writing. Overall, the use of abbreviations is a common practice in mathematical writing and provides a concise and standardized way to refer to theorems and other related statements. It allows for efficient communication and understanding of mathematical arguments, while also respecting the historical and foundational contributions of mathematicians.。