Area I
Order, numbers, sets, categories, models — the language everything else is written in.
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Pathway I
Comparability is optional. Hasse diagrams and the lattices they generate.
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Pathway II
Add infinities to the line. Extended reals and the compactification that makes ±∞ points.
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Pathway III
Primes, wrapping clocks, and the spiral that grows from adding the last two terms.
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Pathway IV
Membership and power sets, then size after bijection, then the continuum.
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Pathway V
Objects and arrows. Composition, commutative squares, and Yoneda’s lemma.
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Pathway VI
Structures interpret symbols. Compactness: finite consistency is enough.
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