Sentence examples for exactly the same elements from inspiring English sources

It is possible that Si and Sj, i ≠ j, may have exactly the same elements and are distinguished only by the indices i, j.

Thus, two sets are equal if and only if they have exactly the same elements.

This will include exactly the same elements as for those patients who were allocated to the conservative treatment.

EDXA spectra of lung tissue did not indicate exactly the same elements present in original glass fibers.

Research the same elements.

They had the same elements".

However, it is important to note that none of any waste stream (to be) considered has exactly the same chemical or element composition as the production organism and its product(s), including, e.g., CO2.

Suppose L is a first-order language, T is a theory in L, and Φ is a set of formulas of L. We say that T has elimination of quantifiers down to Φ if for every formula φ x1,…,xn) of L there is a formula ψ x1,…,xn) in Φ such that in every model of T, φ and ψ are satisfied by exactly the same n-tuples of elements (a1,…,an).

Obviously, exactly the same linear combination of the elements of (g_{yy}^{-1}(lambda )partial g_{yy}(lambda )/partial {varvec{theta }}) will be singular too.

Further, according to Koichi Ishii the games do not take place in exactly the same world, and characters or elements who appear in different titles are best considered alternate versions of each other.

The game is not a direct sequel to the events in Secret of Mana; according to series creator Koichi Ishii, the Mana games do not take place in exactly the same world, and characters or elements who appear in different games are best considered alternate versions of each other; instead, the connections between each title are more abstract than story-based, linked only on the karmic level.