Particularly, if we choose α-generator I, the identity function α ( x ) = x for all x ∈ R ⇒ α − 1 ( x ) = x, then obviously α-arithmetic turns out to be classical arithmetic.
"The key point is that numbers are spelled differently and are longer in Welsh than in English, and it turns out that memory (and arithmetic) depend on how easily pronounced the words are.
Now of course the administration is trying to use California's woes to sell its plan to drill for oil in the Arctic tundra -- a plan that, if you do the arithmetic ("No fuzzy math!" roared the crowd), turns out to be virtually irrelevant to our current energy problems.
For example, the Axiom of Choice allows the taking of maximal ideals in rings and other structures; it entails the kinds of maximality principles that even the analysts were already using; it simplifies transfinite arithmetic; and despite its suspicious abstractness it turns out to be equivalent to 'concrete' and 'mathematical' statements such as the claim that every vector space has a basis.
People power turns out to be about politics, not arithmetic.
It turns out, however, that the principles of arithmetic can be derived without Frege's definition.
After all, haven't economists proved that economic growth collapses once public debt exceeds 90 percent of G.D.P.? Well, the famous red line on debt, it turns out, was an artifact of dubious statistics, reinforced by bad arithmetic.
However the election turns out, the reaction to the debates made it clear that voters have a visceral dislike for candidates who seem intellectual, let alone try to make the electorate do arithmetic.
It turns out that the real secret of success in the information age is what it always was: fundamentals -- reading, writing and arithmetic, church, synagogue and mosque, the rule of law and good governance.
