Similarly, the subset order ⊆ on the subsets of any given set is antisymmetric: given two sets A and B, if every element in A also is in B and every element in B is also in A, then A and B must contain all the same elements and therefore be equal:

Similarly, given any element y of Y, there is a function f < sub > y </ sub >, or f (·, y ), from X to Z, given by f < sub > y </ sub >( x ) := f ( x, y ).

Similarly, for any a in F other than 0, there exists an element a < sup >− 1 </ sup > in F, such that a · a < sup >− 1 </ sup > = 1.

Similarly, in the power formulation, power can be distributed by generating a set of rays from the radiating element in the same way, and spreading the power to be distributed equally between each element a ray hits.

Similarly, as romance has become a common element of many shōjo works, any title with romance, such as the shōnen Love Hina

Similarly, if every preimage of a base element of Y is open in X, then f is continuous.

Similarly, to validate that each element has an acceptable sequence of child elements, information about what child elements have been seen for each parent, must be kept until the parent closes.

Similarly, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.

* Similarly, a thin heating element

An interpretation of a constant symbol of σ in M is simply an element of M. More generally, an interpretation of an n-ary function symbol f is a function from M < sup > n </ sup > to M. Similarly, an interpretation of a relation symbol R is an n-ary relation on M, i. e. a subset of M < sup > n </ sup >.

Similarly, including a " p " element within the content of an " em " element is also invalid.

Similarly, an ideal voltage source cannot be connected to an ideal short circuit ( R = 0 ), since this would result a similar paradox of finite nonzero voltage across an element with defined zero voltage ( the short circuit ).

When this occurs, A must be the largest antichain in the order, for any antichain can have at most one element from each member of P. Similarly, P must be the smallest family of chains into which the order can be partitioned, for any partition into chains must have at least one chain per element of A.

Similarly, the elements of a list can have values of any type and these can be different from element to element within the list.

Similarly Freud concluded that ' we can detect an element of megalomania in most other forms of paranoic disorder.

Similarly, the identity path component of a topological group G is the path component of G that contains the identity element of the group.

Similarly, a stamp consisting of simply a portrait will mean little to many users, and the artist may opt to include a visual element suggesting the person's accomplishments, such as an architect's most famous building, or simply add the word " architect " somewhere in the design.

Similarly, this can explain the transition from conductor to insulator in systems such as rare-earth pyrochlores as the atomic number of the rare-earth metal increases, because the lattice parameter increases ( or the angle between atoms can also change — see Crystal structure ) as the rare-earth element atomic number increases, thus changing the relative importance of the hopping integral compared to the onsite repulsion.

Similarly, a key element in Shadow of the Colossus is the relationship between Wander and his horse, Agro.

Similarly, products of the gammas such as γ < sub > μ </ sub > γ < sub > ν </ sub > represent oriented surface elements, and so on.

Similarly, as an infinite-dimensional example, the Lebesgue space L < sup > p </ sup > is always a Banach space but is only a Hilbert space when p = 2.

Similarly, if we limit the number of literals per clause to 2 and change the OR operations to XOR operations, the result is exclusive-or 2-satisfiability, a problem complete for SL = L.

Similarly, < tt >( λx. y ) s → y := s = y </ tt >, demonstrating that < tt > λx. y </ tt > really is a constant function.

Similarly, there are φ ( 10 ) =

Similarly to the use of NP-complete problems to analyze the P = NP question, the P-complete problems, viewed as the " probably not parallelizable " or " probably inherently sequential " problems, serves in a similar manner to study the NC = P question.

The logic behind this is analogous to the logic that a polynomial-time solution to an NP-complete problem would prove P = NP: if we have a NC reduction from any problem in P to a problem A, and an NC solution for A, then NC = P. Similarly, if we have a log-space reduction from any problem in P to a problem A, and a log-space solution for A, then L = P.

Similarly, metal ion hydrolysis causes ions such as < span style =" white-space: nowrap ;">< sup > 3 +</ sup ></ span > to behave as weak acids :< ref name = Burgess > Section 9. 1 " Acidity of Solvated Cations " lists many pK < sub > a </ sub > values .</ ref >

This can only happen if Q is an m × n matrix with n ≤ m. Similarly, QQ < sup > T </ sup > = I says that the rows of Q are orthonormal, which requires n ≥ m.

Since a Fahrenheit-sized interval of temperature is only < sup > 5 </ sup >⁄< sub > 9 </ sub > that of a Celsius-sized interval, the value is typically expressed as 10. 4 ( µin / in )/° F rather than 18. 7 ( µin / in )/° C .< sub > </ sub ></ ref > Similarly, a metering pump that injects a trace chemical into the main process line at the proportional flow rate Q < sub > p </ sub > = 125 ppm, is doing so at a rate that may be expressed in a variety of volumetric units, including 125 µL / L, 125 µgal / gal, 125 cm < sup > 3 </ sup >/ m < sup > 3 </ sup >, etc.

Similarly organic compounds with single C-C-bonds elute later than those with a C = C or C-C-triple bond, as the double or triple bond is shorter than a single C-C-bond.

Similarly, if b ≠ 0, the normal plane at ( 0, b, 0 ) is the plane of equation y = b.

Similarly, for a fixed complex unit u = exp ( b i ), the equation:

Similarly, if g and h are elements of a finite cyclic group G then a solution x of the equation g < sup > x </ sup > = h is called a discrete logarithm to the base g of h in the group G.

Similarly k = g < sup >– p </ sup > ( mod N ) for any non-zero index k and for a unique p in 0 ,..., N – 2, where the negative exponent denotes the multiplicative inverse of g < sup > p </ sup > modulo N. That means that we can rewrite the DFT using these new indices p and q as:

Similarly, 136, 948 is a vampire because 136, 948 =

Similarly, for every point on the radical axis of circles 2 and 3, the powers must be equal, h < sub > 2 </ sub > = h < sub > 3 </ sub >.

For example, the representation < tt > 022. 101. 031. 153 </ tt >, when parsed as octal, would be equivalent to the decimal notation < tt > 18. 101. 25. 153 </ tt >.< ref group = note > Similarly, standard IP addresses can be written with a leading 0x to mean a hexadecimal address: pinging < tt > 133. 45. 0xEE. 0x10 </ tt > pings the decimal address < tt > 133. 45. 238. 16 </ tt >.</ ref >

Similarly, any multiple of four is a difference of the squares of two numbers that differ by two: ( k + 2 )< sup > 2 </ sup >-k < sup > 2 </ sup > = 4k + 4.

Similarly, a right R-module M is flat if and only if Tor < sub > n </ sub >< sup > R </ sup >( M, X ) = 0 for all and all left R-modules X.

# Similarly add 7 + 5 =

Similarly IF A > B THEN A ← A − B.

Similarly, because meters per second, the expression f ′( g ′( 10 )) represents the change in pressure at a height of − 98 meters per second, which is also nonsense.

Similarly, if Alice gets − z, Bob will get + z.

Similarly, if Alice's measurement result is − z, the system undergoes an orthogonal projection onto

Similarly, for any semi-normed vector space we can define the distance between two vectors u and v as ‖ u − v ‖.

Similarly, if n is divisible by 3, and m was already a prime distinct from 3, then n − m would also be coprime to 3 and thus be slightly more likely to be prime than a general number.

# Similarly, pleasure's opposite − pain − is universally avoided, which provides additional support for the idea that pleasure is universally considered good.

Similarly, a skew-symmetric matrix is determined by n ( n − 1 )/ 2 scalars ( the number of entries above the main diagonal ).

Similarly, the star will never rise above the local horizon if δ − θ is less than − 90 ° ( observer in northern hemisphere ), or δ − θ is greater than + 90 ° ( observer in southern hemisphere ).

* Similarly, the free group F < sub > n </ sub > has p < sup > n </ sup > − 1 subgroups of index p.

Similarly, a function has a local minimum point at x < sup >∗</ sup >, if f ( x < sup >∗</ sup >) ≤ f ( x ) when | x − x < sup >∗</ sup >| < ε.

Similarly, the number of k-dimensional faces or bounded faces can be read off as the coefficient of x < sup > n − k </ sup > in (− 1 )< sup > n </ sup > w < sub > A </ sub > (− x, − 1 ) or (− 1 )< sup > n </ sup > w < sub > A </ sub >(− x, 1 ).

Similarly, with the exception of 5, a safe prime q is of the form 4k − 1 or, equivalently, q ≡ 3 ( mod 4 ) — trivially true since ( q − 1 ) / 2 must evaluate to an odd natural number.

Similarly, the greatest negative value for the AO since 1950 in January was − 3. 767 in 1977, which coincided with the coldest mean January temperature in New York City, Washington, D. C., Baltimore, and many other mid-Atlantic locations in that span of time.