Sentence examples for are both equivalent from inspiring English sources

It is well known that the Ekeland variational principle [1] and Caristi-Kirk fixed point theorem are both equivalent.

The rule above is equivalent to ⊢ OB-OD in any system with OB-RE, and in fact, in the context of SDL, these are both equivalent to OB-NC.

The principles DAC\ _X\) and DAC\(^*_X\) are dual forms of the axiom of choice for \(X\): classically they are both equivalent to AC\ _X\) and AC\(^*_X\) but intuitionistically DAC\(^*_X\) implies DAC\ _X\), and not conversely.

Thus, each transformation results in an expression that is mathematically equivalent to the first (in this case, (100 − 1) × 3 and 300 − 3 are both equivalent to 99×× 3).

It is easy to see that the first inequality in (5.10) when (lambda =0) and the second inequality in (5.10) when (mu=0) are both equivalent to sum aR_{1}gesum(b+c)r_{1}, (5.11) which follows from (4.13).

A high positive weight of an edge suggests a high likelihood that the two pairs of A-D points are both equivalent pairs.

They were both equivalent strains (Von Mises strains).

Sentences ψ and χ are logically equivalent if they are both truth equivalent and falsity equivalent.[28] Due to the failure of bivalence, in IFL truth equivalence does not guarantee logical equivalence.

We should introduce three-, five- and seven-year apprenticeships that are both the equivalent to degrees and vocational for those who are not as academically minded.

For example, every two accepted input configurations are equivalent, because both are equivalent to (s_{mathrm {acc}}).

In other words, they are equivalent or "both theories do the same thing".