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It is sometimes desirable to prove a statement involving two natural numbers, n and m, by iterating the induction process. That is, one proves a base case and an induction step for n, and in each of those proves a base case and an induction step for m. See, for example, the proof of commutativity accompanying addition of natural numbers. More ...
A closing argument, summation, or summing up is the concluding statement of each party's counsel reiterating the important arguments for the trier of fact, often the jury, in a court case. A closing argument occurs after the presentation of evidence. A closing argument may not contain any new information and may only use evidence introduced at ...
The summation of an explicit sequence is denoted as a succession of additions. For example, summation of [1, 2, 4, 2] is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative, there is no need for parentheses, and the result is the same irrespective of the order of the summands ...
Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory.
Few things will put a damper on your vacation or holiday faster than food poisoning.The intense stomach pain, rushing to the toilet and feeling relegated to bed keeps just about everyone out of ...
In mathematical analysis, Cesàro summation (also known as the Cesàro mean [1] [2] or Cesàro limit [3]) assigns values to some infinite sums that are not necessarily convergent in the usual sense. The Cesàro sum is defined as the limit, as n tends to infinity, of the sequence of arithmetic means of the first n partial sums of the series.
A Florida woman who said she was playing a game with her boyfriend when she zipped him up in a suitcase and left him to die has been sentenced to life in prison.
The current average interest rate for a 30-year fixed mortgage is 6.80% for purchase and 6.80% for refinance — up 7 basis points from 6.73% for purchase and 5 basis points from 6.75% for ...