Infinity and Mathematics
Mathematics is a playground of infinity — or better, of many infinities. Infinitely many! The following articles offer a crash course in all aspects of mathematical infinity.
BanachTarski paradox: Gold bars out of nothing.
Berry paradox: The unnamable numbers.
Cantor: Pope and heretic of infinity.
Cantor dust: How to spend 80% and yet retain 100%.
Cardinals: Numbers that are none.
Cartesian coordinates: Topography of points.
Chaos: Minor cause, major effect. What chaos theory is about and why it does not exist.
Continuum hypothesis: The greatest puzzle and its astonishing solution.
Countability: How to count the infinite.
Dimensions: More points in a surface than in a line?
Endless loop: Turing's discovery, or why programmers do not find any bugs.
Finitism: The inquisitors of mathematics.
Fractals: Norway and cauliflower.
Functions: Growth beyond all limits.
Galilei's paradox: The second greatest terror for Galileo Galilei.
Hilbert's hotel: How to obtain a room in a fully booked hotel.
Infinitesimal calculus: The mathematics that can't actually work.
Infinity: Philosophers against mathematicians.
Lemniscate: Construct of infinity.
Library of Babel: Books that contain everything and therefore nothing.
Numbers: That's the issue here.
Number of grains of sand: Archimedes counts the uncountable.
Number line: An infinite fragile construct.
Number systems: They save you the need for an infinite memory.
Ordinal numbers: How to count beyond the infinite.
Parallels: Determine the curvature of space.
Pi: The most magic of all numbers?
Primes: An unsolved mystery.
Recursions: Loops of infinity.
Russell's paradox: Why a barber cannot shave himself.
Sequences: From zero to infinity.
Singularity: A kink in the curve.
Symbols of Infinity: The oldest symbols of humankind.
Thoughts: The set of all thoughts is infinite.
Truth: Why there can't be any.
Unboundedness: Can indeed be finite.
Wallis: Rediscoverer of infinity.
Zenon's paradox: Beginning and end of infinity.
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