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  • ...of [[Peano arithmetic]]. In other words, <math>S</math> is the set of all arithmetic statements. We know that some of these statements are provably equivalent
    4 KB (717 words) - 19:01, 25 April 2009
  • ...ator]]s, arranged in a sensible way. Thus, <math>3 - \frac x4</math> is an arithmetic expression, while <math>7 \times + 43</math> is not. There are no equal sig ...in finding equivalences between expressions of various sorts. In standard arithmetic, for instance, the two expressions <math>(3x + 4) - x + 2</math> is equival
    2 KB (239 words) - 13:42, 11 March 2023
  • The arithmetic mean (average) of four numbers is <math>85</math>. If the largest of these Pat Peano has plenty of 0's, 1's, 3's, 4's, 5's, 6's, 7's, 8's and 9's, but he has on
    14 KB (1,797 words) - 10:13, 28 December 2022
  • ...any axiomatic theory <math>F</math>, which can prove anything that [[Peano arithmetic]] can, is either inconsistent (i.e. it can both prove and disprove any give
    2 KB (279 words) - 11:09, 28 September 2024
  • ...e strengths of various system. For example the ordinal strength of [[Peano arithmetic]] is <math>\varepsilon_0</math>, which makes it one of the weakest systems ...rdinal, which means it is unprovable in Kripke-Platek set theory and Peano arithmetic. As another example, consider Gabriel Nivasch's ''fusible numbers <math>\ma
    5 KB (811 words) - 13:16, 7 June 2020