The proof of this theorem consists essentially of a formalization in arithmetic of the arithmetized version of the proof of the statement, "If a system is consistent, then p is not provable"; i.e., it consists of a derivation within number theory of p itself from the arithmetic sentence that says that the system is consistent.
We can extend our earlier observation that it is not definable in second-order arithmetic; it is not definable in arithmetic of higher order either.
Thereafter, T-test was conducted to verify the significance of difference in arithmetic means values of the driving and exhaust characteristics of the measured variables.
Like most people who play similar roles in primary campaigns, Mr. Boyle and Mr. Romaine are deeply rooted locally — experts in the arithmetic of election districts, party registration, neighborhood voting patterns and the intangibles that push voters toward one candidate or another.
In the arithmetic of compounding, 20 times 5% equals not 100% but 64%.
And in arithmetic, 73.6% of boys reached at least the expected level of development, compared with 81.4% of girls.
There are four story types in arithmetic word problems of addition and subtraction: (1) combination, (2) increase, (3) decrease, and (4) comparison (Riley et al. 1983).
Our findings indicate a dissociation in prefrontal and parietal cortex function during arithmetic processing and further provide the first evidence for a specific role for the angular gyrus in arithmetic computation independent of other processing demands.
We studied the role of syntax in arithmetic thinking, a neglected component of numerical cognition, by examining eye movement sequences during the calculation of arithmetic expressions.
The change in brain activation patterns observed was similar to the results of previous neuroimaging studies investigating training effects in arithmetic after a week of extensive training.
This also easily yields a weak version of the incompleteness result: the set of sentences provable in arithmetic can be defined in the language of arithmetic, but the set of true arithmetical sentences cannot; therefore the two cannot coincide.
