Sentence examples for example a proof from inspiring English sources
For example, a proof that \(∀ x, P x)\) often starts with "choose an arbitrary \(x\)." See the fa15 notes for a systematic list of proof structures.
This philosophy has its origins in the earlier work of the Dutch mathematician-logician L.E.J. Brouwer, who criticized "mainstream" mathematical logicians for accepting proofs that mathematical objects exist without there being any specific construction of them (for example, a proof that some series converges without any specification of the limit which it converges to).
Often these strategies (or their existence) turn out to be equivalent to something of logical importance that could have been defined without using games for example a proof.
For example, a proof of B from A is considered valid, if every closed proof, which is obtained by replacing the open assumption A with a closed proof of A, is valid.
In this scenario, the IDS still performs the same function of identifying patterns of malicious behavior on a system that may be compromised [24]; for example a proof of concept based on the Snort IDS successfully prevented a Distributed Denial of Service (DDoS) attack [25].
For example, a proof-theoretic analysis may contribute to establish whether a certain theory complies with a given mathematical framework (e.g., predicativity, finitism, etc).
We describe the SCA approach and provide a detailed example as a proof of concept of its use for the analysis of nurse handoff communication in a medical intensive care unit.
For example, in a proof of concept study, known mutations and artificial variants in exon18 BRCA1 were introduced using the CRISPR/Cas9 technique, resulting in traceable changes in BRCA1 mRNA splicing and abundance [ 43].
These examples are a proof of concept.
This report provides a wonderful example of a proof-of-concept study indicating that FMT may represent an ideal therapeutic alternative to control systemic inflammation in patients with sepsis.
This example serves as a proof of principle for the DiCE approach and it also demonstrates that method can highlight reasonable directions for future research (see Additional file 1).
