Hurrah! Hurray! Long live Inteland!

I got an elegant way (efficient, algebraic!) to introduce the multiplication of integers. Actually more than that. The common approach works not only for Inteland (integers) but also for all cyclands. Thus the conceptual sequence is:

minusop   ⇒   cycland   Inteland

It’s 2012, and to spend time on foundations of integers may seem silly. Nevertheless it was worth it! Technically, everything is easy, virtually trivial (especially after it’s done). But my Inteland (no more “InteGland”, no more “G”) has conceptual value, it allows regular mathematicians to have a good feeling about it, it has value for education. Inteland means a mild but nice breakthrough since the times of Peano and Hilbert. The topic in the past was so tedious that only logicians cared about it. No textbook on number theory would bother to introduce integers (or natural numbers) thoroughly. They would say this and that about induction and perhaps a few words about commutativity and associativity (?), and otherwise they would rely on the reader’s good intuition of natural numbers.
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Enough of this shameless self-praising. It’s time to write all of it again from scratch. Should I go to Starbucks at Arborland. I am at the Glenco Crossing shopping center, as usually. The one at Arborland is open 24h/day all year except for the X’mass.

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