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"God made the integers; all the rest is the work of Man." ~ Leopold Kronecker, when criticizing Cantor's work [0]. See also Stephen Hawking's Anthology by a sim
by daveslash 4y ago
"God made the integers; all the rest is the work of Man." ~ Leopold Kronecker, when criticizing Cantor's work [0]. See also Stephen Hawking's Anthology by a similar name. [1]
[0] https://en.wikipedia.org/wiki/Leopold_Kronecker https://en.wikipedia.org/wiki/Leopold_Kronecker
[1] https://en.wikipedia.org/wiki/God_Created_the_Integers https://en.wikipedia.org/wiki/God_Created_the_Integers
- another_devy 4y agoGod should have made uint. I don’t want to deal with all these negativity
- bediger4000 4y agoThat's an argument from authority isn't it? Rational numbers are pretty easy to understand. There are easy to understand proofs that at least some irrational numbers (famously square root of 2) exist. That is, the square root of 2 cannot be represented as a rational number. I'm sure there are other such proofs. My take is that Kronecker and Hawking were either making an ironic statement or just expressing irony or exasperation.
- constantcrying 4y agoI think you are missing the point. Kronecker does not deny that irrational numbers exist, he states his belief that the fundamental number system which is inherent to reality are the natural numbers. That (by divine authority) are the irreducable thing which other number system must take from. E.g. the rationals are pairs of natural numbers, the reals cauchy sequences of rational numbers etc. > I'm sure there are other such proofs. The reals are uncountable.