The phrase "always equivalent" is correct and usable in written English.
It can be used in contexts where you want to express that two or more things are consistently equal in value, meaning, or function.
Example: "In mathematics, the two expressions are always equivalent, regardless of the values assigned to the variables."
Alternatives: "consistently equal" or "invariably the same".
If β is the result of relettering a bound variable in a wff α, then α and β are said to be bound alphabetical variants of each other, and bound alphabetical variants are always equivalent.
The stable manifold is always equivalent to.
Everyday thinking is not always equivalent to scientifically accepted concepts.
However, the understanding of the term "quality" among involved participants is not always equivalent.
No, the amount of loss is always equivalent to the amount of greed.
As mentioned in [15, 16], local field neural networks and SNNs are not always equivalent.
However, when selling to non-Anglophile countries there isn't always an equivalent word in the language so it's not clear what we do from our branding.
It assumes that if you have a conceptual thing named x it must always be equivalent to itself, that it has a uniqueness about it, that it is in possession of something so irreducible that we must assume it is absolutely, unchangeably equivalent to itself for all time, that its very elementalness can never be altered.
It turns out that for any Hopf algebra such that (V) is of finite dimension these formal power series all converge in a neighbourhood (U) of the origin in (Vtimes V) and thus give an analytic map begin{aligned} Vtimes Vsupseteq Urightarrow V. end{aligned}This map is, in fact, a finite-dimensional local Lie group and these are always locally equivalent to simply-connected Lie groups.
However, orthologous genes are not always functionally equivalent.
Rice (Oryza sativa) proteins also exhibit functional differentiation, although they are not always functionally equivalent to their Arabidopsis homologues.
