For example, a seated passenger in a moving airplane has zero kinetic energy relative to the airplane, but non-zero kinetic energy ( and higher total energy ) relative to the Earth.

For a discrete probability function f ( y ), let y < sub > i </ sub >, i = 1 to n, be the points with non-zero probabilities indexed in increasing order ( y < sub > i </ sub > < y < sub > i + 1 </ sub >).

For example, JUMPN A, LOC jumps to the address LOC if the contents of register A is non-zero.

For a continuous random variable, the probability of any specific value is zero, whereas the probability of some infinite set of values ( such as an interval of non-zero length ) may be positive.

For a non-zero formal Laurent series, the minimal integer n such that a < sub > n </ sub >≠ 0 is called the order of f, denoted ord ( f ).

For a positive normalised number it can be represented as m < sub > 0 </ sub >. m < sub > 1 </ sub > m < sub > 2 </ sub > m < sub > 3 </ sub >... m < sub > p-2 </ sub > m < sub > p-1 </ sub > ( where m represents a significant digit and p is the precision, and m < sub > 0 </ sub > is non-zero ).

For this reason, the pressure of a Fermi gas is non-zero even at zero temperature, in contrast to that of a classical ideal gas.

For this case of an axisymmetric flow, the only non-zero component of the vorticity vector ω is the azimuthal φ – component ω < sub > φ </ sub >

For another way to view this example, notice that according to classical logic, if the locally non-zero condition fails, then it must fail at some specific point x ; and then f ( x ) will equal 0, so that IVT is valid automatically.

For functions of more than one variable, the theorem states that if the total derivative of a continuously differentiable function F defined from an open set U of R < sup > n </ sup > into R < sup > n </ sup > is invertible at a point p ( i. e., the Jacobian determinant of F at p is non-zero ), then F is an invertible function near p. That is, an inverse function to F exists in some neighborhood of F ( p ).

For a given pair of real symmetric positive-definite matrices, and a given non-zero vector, the generalized Rayleigh quotient is defined as:

For a diagonal matrix such as, we get the pseudoinverse by taking the reciprocal of each non-zero element on the diagonal, leaving the zeros in place, and transposing the resulting matrix.

For example, in the codimension 1 case, we can define the tangent bundle of the foliation as, for some ( non-canonical ) ( i. e. a non-zero co-vector field ).

For example in the surface case, an everywhere non-zero vector field can exist on an orientable compact surface only for the torus.

For example, the ring Zy /( xy ) contains x + ( xy ) and y + ( xy ) as zero divisors, but no non-zero nilpotent elements.

* For any non-zero invariant vector in a rational representation on G, there is an invariant homogeneous polynomial that does not vanish on it.

For S is a pure state if and only if its diagonal form has exactly one non-zero entry which is a 1.

For instance, one must presuppose some degree of indeterminate future behavior in any telecommunications systems to achieve non-zero entropy ( if one already knows what the other person will say one cannot learn anything ).

For non-zero cosmological constants, on curved spacetimes quantum fields lose their interpretation as asymptotic particles.

For regular binary representations of values, half of all bits will be non-zero, on average, but with NAF this drops to only one-third of all digits.

For a given connected graph G with n labeled vertices, let λ < sub > 1 </ sub >, λ < sub > 2 </ sub >, ..., λ < sub > n − 1 </ sub > be the non-zero eigenvalues of its Laplacian matrix.

* For α a non-zero limit ordinal, the Morley rank is at least α if it is at least β for all β less than α.

In fact that statement is a little weaker, in that it disregards any initial partial sum of the series, in a way that may vary according to p. For the other primes the radius is non-zero.

For example, a 2 × 2 matrix describing a 45 ° rotation will not leave any non-zero vector pointing in the same direction.

; Closure: For all a, b in A, the result of the operation a • b is also in A.

; Associativity: For all a, b and c in A, the equation ( a • b ) • c = a • ( b • c ) holds.

; Inverse element: For each a in A, there exists an element b in A such that a • b

; Commutativity: For all a, b in A, a • b = b • a.

For positive values of a and b, the binomial theorem with n = 2 is the geometrically evident fact that a square of side can be cut into a square of side a, a square of side b, and two rectangles with sides a and b. With n = 3, the theorem states that a cube of side can be cut into a cube of side a, a cube of side b, three a × a × b rectangular boxes, and three a × b × b rectangular boxes.

For example, the formula a AND b is satisfiable because one can find the values a = TRUE and b = TRUE, which make ( a AND b ) = TRUE.

For given nonzero integers a and b there is a nonzero integer of minimal absolute value among all those of the form ax + by with x and y integers ; one can assume d > 0 by changing the signs of both s and t if necessary.

For example, in 1988 the United Church of Canada, that country's largest Protestant denomination, affirmed that " a ) All persons, regardless of their sexual orientation, who profess Jesus Christ and obedience to Him, are welcome to be or become full member of the Church ; and b ) All members of the Church are eligible to be considered for the Ordered Ministry.

For an edge type, b is perpendicular to the dislocation line, whereas in the cases of the screw type it is parallel.

For example, the Bourbaki group adopted a watered-down and selective version of it as adequate to the requirements of their twin projects of ( a ) writing encyclopedic foundational works, and ( b ) supporting the axiomatic method as a research tool.

For example, suppose a and b are two sensible objects in a certain situation of affairs.

For this change is not a change from one positive position to another, but a change from order and truth to disorder and negation.

For example, one study on volunteerism found that feeling overwhelmed by others ' demands had an even stronger negative effect on mental health than helping had a positive one ( although positive effects were still significant ).

Also, supporters of this view would characterize Luke ’ s portrayal of the Roman Empire as positive because they believe Luke “ glosses over negative aspects of the empire and presents imperial power positively .” For example, when Paul is before the council defending himself, Paul says that he is “ on trial concerning the hope of the resurrection of the dead ” ( Acts 23: 6 ).

For many applications where one is only concerned about rotation around one axis, it is sufficient to discard the pseudovector nature of angular momentum, and treat it like a scalar where it is positive when it corresponds to a counter-clockwise rotation, and negative clockwise.

* For a finite field of prime order p, the algebraic closure is a countably infinite field which contains a copy of the field of order p < sup > n </ sup > for each positive integer n ( and is in fact the union of these copies ).

For example, is a positive literal and is a negative literal.

For example, if an electric field is placed across a solution of Na < sup >+</ sup > and Cl < sup >−</ sup > ( and conditions are right ) the sodium ions move towards the negative electrode ( cathode ), while the chloride ions move towards the positive electrode ( anode ).

For example, the Daniell galvanic cell's copper electrode is the positive terminal and the cathode.

For example, reversing the current direction in a Daniell galvanic cell would produce an electrolytic cell, where the copper electrode is the positive terminal and the anode.

For a given material, it can have a positive or negative sign or exceptionally it can be zero, and this can depend on the temperature, as it does for water about 4 C. The concept of latent heat with respect to volume was perhaps first recognized by Joseph Black in 1762.

For the simple electric dipole given above, the electric dipole moment points from the negative charge towards the positive charge, and has a magnitude equal to the strength of each charge times the separation between the charges.

For larger values of n, Fermat's Last Theorem states there are no positive integer solutions ( x, y, z ).</ td >

For example, air pollution may generate a negative externality, and education may generate a positive externality ( less crime, etc .).

For any positive integer n, the set of all n-tuples of real numbers forms an n-dimensional vector space over R, which is denoted R < sup > n </ sup > and sometimes called real coordinate space.

For a reason that was not recorded, he identified the term " positive " with vitreous electricity and " negative " with resinous electricity.

For example, one of the most recent results is that, even after subtracting the positive influence of decadal variation, shown to be possibly present in the ENSO trend, the amplitude of the ENSO variability in the observed data still increases, by as much as 60 % in the last 50 years.

For closed ( orientable or non-orientable ) surfaces with positive genus, the maximum number p of colors needed depends on the surface's Euler characteristic χ according to the formula

For s-polarization, a positive r or t means that the electric fields of the incoming and reflected or transmitted wave are parallel, while negative means anti-parallel.

For p-polarization, a positive r or t means that the magnetic fields of the waves are parallel, while negative means anti-parallel.

* For every prime number p and positive integer n, there exists a finite field with p < sup > n </ sup > elements.

For example, the set of all positive integers is infinite:

For any positive integers and, there exists a graph with girth at least and chromatic number at least ; for instance, the Grötzsch graph is triangle-free and has chromatic number 4, and repeating the Mycielskian construction used to form the Grötzsch graph produces triangle-free graphs of arbitrarily large chromatic number.

For complex numbers with a positive real part, it is defined via an improper integral that converges: