Sentence examples for proofs such from inspiring English sources

Much of the rest of the week was spent nailing down the general case of the problem with proofs (such as this inductive one by Patrick C) and algorithms (a histogram integrator by Giovanni Ciriani and Dr W).

Mathematical proofs such as the proof of Gödel's incompleteness theorem are also long and complicated.

Existing security mechanisms for in-network aggregation often introduce considerable additional overhead, resulting from cryptographic proofs, such as signatures.

Mathematicians have presented different proofs, such as [4 6], to the original Erdös-Mordell inequality and some generalizations [7, 8].

(Actual proofs such as the ε-substitution had always been of such a kind: provide finitary procedures which eliminate transfinite elements from proofs of real statements, in particular, of 0 = 1).

The systems discussed are certainly more capable than this and some have been used to assist in the formalization of far more advanced proofs such as Erdös-Selberg's proof of the Prime Number Theorem (about 30,000 lines in Isabelle), the formalization of the Four Color Theorem (60,000 lines in Coq), and the Jordan Curve Theorem (75,000 lines in HOL Light).

A mathematical proof, such as Zhang produced, "should resemble a simple and clear-cut constellation," he wrote, "not a scattered cluster in the Milky Way".

Proof such as a marriage certificate is required, but the cruise does not have to include the wedding date; (800) 222-1236 or www.fcwl.com.

If you can establish with some proof, such as the receipt, that it was bought there, that's the first hurdle cleared.

Wherever other forms of bird-proofing, such as spikes and plastic owls, aren't an option — on the façade of a historic building, for example — falconers offer an effective solution.

But hard proof such as artifacts or structures needs to be found to confirm that a society actually inhabited this island, she says.