...le, where it occurs, by a new (for a given expression) variable leads to an expression with the same meaning. For example, in the expressions
...expression, whereas by writing $z$ everywhere instead of $z$ one obtains an expression with exactly the same meaning.
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...le the expression $B$ is called the consequence. The precise meaning of the expression $A\supset B$ differs in the classical, constructive and other approaches to
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...s) of a variable must not lead to an absurd expression. For example, in the expression $ \{ {( x, y) } : {x ^ {2} + y ^ {2} = z ^ {2} } \} $,
respectively, then in the expression $ f ( x, y) $
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...x$ with not more than a countable number of discontinuities has an analytic expression $A(x)$ involving only three operations (addition, multiplication, passing t
If there is at least one analytic expression describing a given function, there are infinitely many such expressions. Th
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A linguistic expression containing variables, in place of which one may substitute propositions, th
Sometimes a propositional form is an expression, constructed in analogy with a [[propositional formula]], in which symbols
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* the algebraic theory of [[regular expression]]s.
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...x$ as the name of the letter $x$, and is using "$x+3=2$" as the name of the expression $x+3=2$. If one says "12 is divisible by 2", then the term "12" is used in
...tors for distinguishing between the autonymous and non-autonymous use of an expression. However, such a differentiation may be difficult in certain cases. Special
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...ere are only axioms at the vertices of the derivation tree, then the formal expression at the end of the derivation is said to be deducible (or derivable) in the
...a derivation must satisfy the same requirement. The concept of a deducible expression in effective formal systems is, generally speaking, not effective.
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...al is equal to the number of permutations of $n$ elements. The more general expression
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A logical operator which serves to form propositions using the expression "for all x" . In formal languages the universal quantifier is most often d
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An expression indicating that one speaks about all $x$ of a measure space $X$ with the po
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...same syntactic structure. A specific axiom scheme is usually realized by an expression $\mathfrak A$ (which is most often formulated in a language different from
...ulated or unambiguously understandable rules for generating axioms using an expression $\mathfrak A$, an axiom scheme is usually referred to as the self-expressio
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(a "quadratic form modulo 2" ). The expression
...e is a symplectic basis on all elements of which $\psi_0$ vanishes; if this expression equals one, then there is a symplectic basis on all elements of which, exce
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...o make up the fraction. The numerator of an algebraic fraction $A/B$ is the expression $A$ (cf. [[Fraction|Fraction]]).
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The expression
The following expression is often also referred to as a symmetric difference:
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...ns, and $x$, $a$, $b$ are variables whose values are real numbers, then the expression $\int_a^bf(x)dx$ is a term with three parameters $a$, $b$, $f$, which denot
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An expression of the form
...the context of constructive logic) restrict the term "sequent" to mean an expression of the form
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...sion $\Gamma\vDash A$ is read as "$\Gamma$ semantically entails $A$" . The expression $\Gamma\vdash A$ is similarly read as "$\Gamma$ syntactically entails $A$"
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The expression "square" for $a\cdot a$ is (just as "cube" for $a\cdot a\cdot a$) a rem
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...umbers $p$ diverges also; see, e.g., [[#References|[a1]]], Thm. 427, for an expression of its partial sums.
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...make up the fraction. The denominator of an algebraic fraction $A/B$ is the expression $B$ (see [[Fraction|Fraction]]).
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The square root of the expression
The expression \eqref{*} itself is sometimes referred to as the mean-squared error or mean
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...equations" also occurs when the system in question is non-linear. By this expression one means a characteristic exponent of the system of equations in variation
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...about their values are called expressions. The first element of a list — an expression $ E $—
...of bound variables that denote the arguments of a function, and exp is the expression that computes the value of a function and contains $ x 1 \dots x n $
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...called the difference. Subtraction is denoted by $-$ (minus). Thus, in the expression
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An element directly following another element; more precisely, the expression "$b$ covers $a$ in the partially ordered set $(P,{<})$" means that $a < b
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...ce and $\mu$ is the mathematical expectation ($\mu$ must be positive). This expression is often used in its percentage form, viz., $V=100\sigma/\mu$ %. This defin
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A logical operation used in forming statements with the expression "for a certain x" ( "an x exists for which", "there exists an x such that
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More generally, an expression of the form $a^b$ is called a power (that of the form $x\to a^x$ a power fu
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The parameter $k$ which enters into the expression of the [[elliptic integral]] in Legendre normal form. For example, in the i
...\theta=k$ is called the modular angle. The modulus $k$ also enters into the expression of the [[Jacobi elliptic functions]], which arise from the inversion of ell
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...mal and minimal extensions]] of an operator defined by a given differential expression on the subspace of functions of compact support. The domains of definition
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The logical operation used for forming the expression "A and B" from two expressions $A$ and $B$. In formalized languages, the
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the expression $ y(m + 1)/y(m) $
The expression $ y (m +1 )/y (m) $
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...sgue space]] $L_p(E)$ with $0<p<1$, in which a quasi-norm is defined by the expression
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The expression
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and the latter is substituted in the expression for $ J( x) $,
The expression $ {J _ {1} } ( {x _ {0} } )( h) $,
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...point $(0,0)$ into a similar Euclidean $(u,v)$-plane. It is the coordinate expression of the bijection $\phi$ generated by the [[Bendixson sphere|Bendixson spher
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The problem of finding an asymptotic expression for
...numbers. Analogous to this problem is the problem of finding an asymptotic expression for
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A numerical factor in an algebraic expression, a known factor in front of a power of an unknown or a constant factor mult
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...is an operation that converts an expression in one logical language into an expression in another while preserving deductive properties. Immersion operations are
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...re satisfied, then $A$ must be true (sufficient conditions). Frequently the expression "necessary and sufficient" is replaced by "if and only if". Necessary an
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...deducible in $S_2$; 2) every axiom of $S_2$ is deducible in $S_1$; 3) if an expression $B$ follows immediately from expressions $A_1,\ldots,A_n$ by virtue of a de
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...sion $P_x'+Q_y'$ has constant sign (i.e. the sign remains unchanged and the expression vanishes only at isolated points or on a curve), then the system \eqref{*}
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A formula that gives an expression for the $n$-th derivative of the product of two functions in terms of their
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...atives, generally taken with a functionally transformed argument. Here, the expression of the functional transformation may include the unknown function, as a res
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then the expression $ A \cdot ( \Delta x) ^ {n} $
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Sometimes, a degree of a number $a$ is an expression of the form $a^b$ where $b$ is also a (suitable) number, see [[Power|Power]
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The differential expression
The expression (1) is sometimes written in the form
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An expression of the form
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The limit of the expression $(1+1/n)^n$ as $n$ tends to infinity:
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