Mathematical Sentence

A Mathematical Sentence is a formal sentence that satisfies a Mathematical Grammar (from a mathematical language).

• AKA: Mathematical Expression.
• Context:
  • It can be a Mathematical Definition.
  • It can include a Mathematical Constant.
  • It can include a Mathematical Variable.
  • It can include a Mathematical Term.
  • It can include a Mathematical Operation.
  • It can include a Mathematical Function.
  • It can be:
    • an Arithmetic Sentence.
    • an Algebraic Sentence(Mathematical Equation).
  • ...
• Example(s):
  • 2 + 3.
  • [math]\displaystyle{ x^2 + 3x − 4 }[/math].
  • x + 2 = 5
  • ...
• Counter-Example(s):
  • a Software Sentence Software Expression.
• See: Constant, Variable, Lambda Calculus, Well-Formed Formula, Mathematical Constant, Variable (Mathematics), Operation (Mathematics), Function (Mathematics).

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References

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Expression_(mathematics) Retrieved:2014-10-4.
  • In mathematics, an expression (or mathematical expression) is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, punctuation, grouping, and other aspects of logical syntax.

2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Mathematical_expression
  • … Being an expression is a syntactic concept – the meaning of the variables is irrelevant, but different fields have different notions of validity.　See formal language for how expressions are constructed, and formal semantics for meaning.
    Common types of mathematical expressions include:
    • arithmetic expressions (e.g. 2 + 3).
    • algebraic expressions such as polynomials (e.g. x^2 + 3x − 4). “rational expressions (e.g. 2 / x + x / 2), and equations (e.g. x + 2 = 5).
  • An expression must be well-formed. That is, the operators must have the correct number of inputs, in the correct places. The expression 2 + 3 is well formed; the expression * 2 + is not, at least, not in the usual notation of arithmetic. Expressions and their evaluation were formalised by Alonzo Church and Stephen Kleene in the 1930s in their lambda calculus. The lambda calculus has been a major influence in the development of modern mathematics and computer programming languages.

• http://planetmath.org/encyclopedia/Sentence.html
  • A sentence is a formula with no free variables. Simple examples include \forall x \exists y [x<y], or \exists z [z+7-43=0]. However the following formula is not a sentence: x+2=3.
• http://planetmath.org/encyclopedia/Expression.html
  • An expression is a symbol or combination of symbols used to denote a quantity or value. Expressions consist of constants, variables, operations, operators, functions, and parentheses. … Note: An equation is a denoted equality of two expressions.
• ipt.byu.edu/~merrillp/jobAids/glossary.htm
  • an expression that evaluates to a numerical value; eg: 45 + Math.random()

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