February 22, 2026
Infinity, but make it spicy
Unreal Numbers
Math fight: ‘real’ numbers go viral as commenters ask if digits can predict the future
TLDR: An explainer on how “real” numbers are built veers into why some digits can’t be computed, tied to the impossible “halting problem.” Commenters bicker over friendly vs rigorous teaching, crack jokes about “future‑predicting” numbers, and insist on algebraic numbers—showing how definitions limit what computers can ever decide.
Math went full soap opera after an explainer on building numbers—from counting 0,1,2 to the bizarre world of “real” numbers—hit Hacker News. The author joked HN once called it “watered down” and “slop,” and the crowd arrived ready. First move: receipts. emmelaich dug up the earlier thread like a reality‑show flashback. Then the memes rolled in: “A number that can predict the future?” quipped koolala, as the piece dove into uncomputable numbers—digits so wild no computer can list them.
The explainers piled on. Reubend took the teacher chair, saying some numbers would solve the “halting problem” (deciding if any program ever finishes), which is famously impossible—so those numbers are uncomputable. Cue gasps. Meanwhile, adrian_b dropped a textbook on the table: don’t skip algebraic numbers—solutions to simple equations—which sit between fractions and the full, messy universe of reals. Translation: there’s more than one kind of “infinite” weird.
The vibe? A split between accessibility fans and the well-actually brigade. Some want friendly stories about infinity; others want every rung on the ladder, neatly labeled. Either way, the thread turned math into popcorn TV: future‑predicting digits, paradox bait, and a reminder that how we define numbers shapes what computers—and we—can do.
Key Points
- •Natural numbers are constructed in Peano arithmetic from zero and a successor function S(…).
- •Addition is defined recursively: a + 0 := a and a + S(b) := S(a + b).
- •Set theory introduces ordinals, with ℕ corresponding to the infinite ordinal ω.
- •Ordinal arithmetic can be non-commutative for infinities, exemplified by ω + 1 ≠ 1 + ω.
- •Cantor’s cardinality groups many infinite ordinals into the same size while distinguishing between ℕ and ℝ.