Sentence examples for arithmetical ones from inspiring English sources
The central problem was thus to justify the use of classical logic in mathematical proofs, arithmetical ones in the first place.
More significant, however, was his use of algebra in developing 'analytic' geometry as it came to be called, which allowed geometrical problems to be transformed into arithmetical ones and more easily solved.
"Logical operations are performed with propositions, arithmetical ones with numbers," says Wittgenstein (WVC 218); "[t]he result of a logical operation is a proposition, the result of an arithmetical one is a number".
It's a cumulative process but never merely an arithmetical one.
We chose instead to compute the rms differences between SV2005, SV2006, SV2007 and SV2008 models on one hand, and their arithmetical mean on the other hand.
This model deals with an arithmetic word problem that is solved using only one arithmetical operation.
In particular there may be complex arithmetical conditions on sets of accessible worlds (role fillers).
The sampling is done by fast interpolation techniques involving only elementary logical and arithmetical operations, allowing one to keep a higher degree of accuracy as the grids spacing is controlled by the user.
The syntactic classes \(\Sigma^b_i\) and \ \Pi^b_i\) are defined in a manner reminiscent to how the classes \(\Sigma^0_i\) and \ \Pi^0_i\) are defined in the traditional arithmetical hierarchy – i.e. by counting alternations of bounded quantifiers, ignoring sharply bounded ones.
Even worse, given an arithmetical sentence (i.e., a sentence not containing T) that can neither be proved nor disproved in PA, one can find a consistent T-sentence that decides this sentence (McGee 1992).
For WCP-COQAM receiver as shown in Figure 9, the arithmetical computation for processing one block of the received data (L=M K samples) can be divided into the computation of one FFT of size L, FDE for one block, polyphase filtering (product of FDE outputs and Gq,m), and IFFTs of size K′ for M subcarriers, noting that the cyclic shift operation does not consume any arithmetical computations.
