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May 2, 2024 · Algebra: The branch of mathematics that substitutes letters for numbers to solve for unknown values. Algorithm: A procedure or set of steps used to solve a mathematical computation. Angle: Two rays sharing the same endpoint (called the angle vertex). Angle Bisector: The line dividing an angle into two equal angles.
- Attribute
An attribute in math is defined as a characteristic of an...
- Algorithm
An algorithm is usually the most efficient (not always) way...
- Binomial
A polynomial equation with two terms usually joined by a...
- Average
Average can mean the mean, the median, and the mode, it can...
- Y-Intercept
Finding the y-intercept of a parabola can be tricky....
- Array
An array is an orderly arrangement (often in rows, columns...
- Angle
Types of Angles . Angles that measure exactly 90 degrees are...
- Base
Definition: The bottom of a shape, solid or three...
- Attribute
The list below has some of the most common symbols in mathematics. However, these symbols can have other meanings in different contexts other than math. If x=y, x and y represent the same value or thing. If x≈y, x and y are almost equal. If x≠y, x and y do not represent the same value or thing. If x<y, x is less than y.
SymbolNameRead AsMeaning=Equalis equal toIf x=y, x and y represent the same value ...≡Definitionis defined asIf x≡y, x is defined as another name of ...≈Approximately equalis approximately equal toIf x≈y, x and y are almost equal.≠Inequationdoes not equal, is not equal toIf x≠y, x and y do not represent the same ...- 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.just made, not to mean“for example”, and is always followed by a comma.) e.g. (exempli gratia) means “for example”. (It is usually used to give an example of a statement that was just made and is always followed by a comma.) viz. (videlicet) means “namely” or “more specifically”’. (It is used to clarify a statement that was
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The ability to understand and make use of higher mathematical jargon. The ability to make sound judgments on the quality and the validity of a proof. The ability to think through the implications of a definition or a proposition. The ability to fill in the preliminaries on one’s own.
A math glossary is a comprehensive list of terms, definitions, and symbols used in mathematics. It serves as a reference for students, teachers, and professionals to quickly look up unfamiliar mathematical concepts and notation. Below are some common mathematical symbols and terms, along with their LaTeX representations and brief explanations.
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An¯ A n ¯ happens for all sufficiently large n n (that is, from some point n0 n 0 onward.) Indeed, if An A n happens for infinitely many n n, then after any given point n0 n 0 there will be some n ≥n0 n ≥ n 0 such that An A n happens (and therefore An¯ A n ¯ does not happen.) Conversely, if An A n only happens for finitely many n n ...
