moments of microscopic fun encountered while studying/researching:
Quantum mechanics call vector space & its dual bra/ket because … bra-c-ket. What can I say? I like it—But where did the letter ‘c’ go, Dirac?
Defining cauchy sequences and limits in real analysis: it’s really cool how you “bootstrap” the definition of Cauchy sequences / limit on real using the definition of Cauchy sequences / limit on rationals. basically:
(1) define Cauchy sequence on rationals
(2) use it to define limit (on rationals) using rational-Cauchy
(3) use it to define reals
(4) use it to define Cauchy sequence on reals
(5) show it’s consistent with Cauchy sequence on rationals in both directions
a. rationals are embedded in reals hence the real-Cauchy definition subsumes rational-Cauchy definition
b. you can always find a rational number smaller than a given real number hence a sequence being rational-Cauchy means it is also real-Cauchy)
(6) define limit (on reals)
(7) show it’s consistent with limit on rationals
(8) … and that they’re equivalent to real-Cauchy
(9) proceed to ignore the distinction b/w real-Cauchy/limit and their rational counterpart. Slick!
Maybe he dropped the “c” because it changes the “a” phoneme from æ to ɑː and gives a cleaner division in sounds: “brac-ket” pronounced together collides with “bracket” where “braa-ket” does not.
moments of microscopic fun encountered while studying/researching:
Quantum mechanics call vector space & its dual bra/ket because … bra-c-ket. What can I say? I like it—But where did the letter ‘c’ go, Dirac?
Defining cauchy sequences and limits in real analysis: it’s really cool how you “bootstrap” the definition of Cauchy sequences / limit on real using the definition of Cauchy sequences / limit on rationals. basically:
(1) define Cauchy sequence on rationals
(2) use it to define limit (on rationals) using rational-Cauchy
(3) use it to define reals
(4) use it to define Cauchy sequence on reals
(5) show it’s consistent with Cauchy sequence on rationals in both directions
a. rationals are embedded in reals hence the real-Cauchy definition subsumes rational-Cauchy definition
b. you can always find a rational number smaller than a given real number hence a sequence being rational-Cauchy means it is also real-Cauchy)
(6) define limit (on reals)
(7) show it’s consistent with limit on rationals
(8) … and that they’re equivalent to real-Cauchy
(9) proceed to ignore the distinction b/w real-Cauchy/limit and their rational counterpart. Slick!
(will probably keep updating this in the replies)
Maybe he dropped the “c” because it changes the “a” phoneme from æ to ɑː and gives a cleaner division in sounds: “brac-ket” pronounced together collides with “bracket” where “braa-ket” does not.