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Rarely, however, it may denote a definition, so it's best to use this symbol only for congruences or identities. In short: $$:=$$ is the most widespread (presumably as it's the easiest to typeset) "by definition" symbol .
May 2, 2024 · Use this glossary of over 150 math definitions for common and important terms frequently encountered in arithmetic, geometry, and statistics.
- Anne Marie Helmenstine, Ph.D.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
The most comprehensive glossary on the jargon of higher mathematics, featuring 106 terms from abstract nonsense to without loss of generality.
- Definitions in Math and in Other Subjects
- Properties of A Math Definition
- Examples of Definitions
- How Definitions Are Worded
- Properties ofMathematical Definitions
- No Standardization
- Imagesand Metaphors For Definitions
- Specifications
- References
"When I use a word, it means just what I choose it to mean--neither more nor less." -- Humpty Dumpty A mathematical definition is fundamentally different in two ways from other kinds of definitions, a fact that is not widely appreciated by students or even by mathematicians. The differences cause students much trouble.
The four rules below are absolute requirementsthat all mathematical definitions obey: 1. LP: The definition consists of a list of some of the propertiesof the concept (and nothing else). 2. EAP: Any example of the concept must have all the propertieslisted in the definition (not just most of them). 3. OAP: Every math object that has all the propert...
A mathematical definition prescribes the meaning of aword or phrase in a very specific way. The word or phrase is defined in terms of a list of required properties (LP), although the list may bedisguised by the wording. In this website, the word or phrase being defined iscalled the definiendum. The phrase thatgives the definition is called the defi...
There are many different ways to word a definition, and thislong section describes a great many of them. You may think that only agrammarian or a dictionary editor would appreciate such infinite attention todetail, but I recommend that you glance through the possibilitieslisted. You may discover 1. Some wordings that you may not recognize as defini...
Every proof originates solely in the definition
The special logical status of a definition (every true statement about the concept follows from the definition) is the reason that rewritingaccording to the definitions is a reasonable first step in comingup with a proof. Here are some seemingly contradictory points about the purple proseabove:
Thereare some very basic words with two common inequivalent definitions, and math texts don't always tell you which definition they are using.Examples:Thereare many, many words and phrases that have one definition that most texts use, but for which some texts give other definitions. For example, "positive" means "greater than zero" in almost all...Certain words and symbols have more than one meaning, and sometimes both those meanings are used in the same document.Certainwords and phrases have a standard meaning in one branch of mathematics and adifferentstandard meaning in another branch.Images and metaphors associatedwith the concept of definition, and the motivation behind theconcept, contribute greatly to understanding definitions, but images and metaphorscannot (directly) be used in proofs.
Because the definition of a math concept can be devious, it may be hard to see how you can use it in aproof. A specification of a mathematical concept is a set of statementsthat are all true of the concept and that suffice for many common uses, butwhich do not characterizethe concept. These are the mainpoints about specifications: 1. Everything the...
Lara Alcock and Adrian Simpson, Ideas from mathematics education, chapter 1.Bills, L., & Tall, D. (1998). Operable definitions in advanced mathematics: The case of the least upper bound. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd Conference of the Internat...B. S. Edwards, and M. B. Ward, Surprises from mathematics education research: Student (mis) use of mathematical definitions (2004). American Mathematical Monthly, 111, 411-424.B. S. Edwards and M. B. Ward,The Role of Mathematical Definitions in Mathematics and inUndergraduate Mathematics Courses.Glossary of mathematical jargon. The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject.
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Illustrated Mathematics Dictionary. Easy-to-understand definitions, with illustrations and links to further reading. Browse the definitions using the letters below, or use Search above.
