Sentence examples for by uniqueness from inspiring English sources

Now, by uniqueness of constants (c_{1}), (c_{2}), we conclude that (2.5) is the unique solution of the boundary value problem (2.3 - 2.4).

"By technological complexity, by importance, by uniqueness.

Therefore, by uniqueness.

Hence x ˜ = x ∗ by uniqueness.

By uniqueness of, we get.

Consequently, x ^ = x ̃ by uniqueness.

that is,, by uniqueness of.

Therefore (bar{x}=x^) by uniqueness.

We get x ¯ = x ∗ by uniqueness.

Hence, x ˜ = x ˆ = x ∗ by uniqueness.

By uniqueness, we have x ′ = x ∗.