carmo55

@carmo55@lemmy.zip

• ⁨Comment⁩ on ⁨What kind of locomotion is that? What is the evolutionary advantage?⁩ ⁨⁨6⁩ ⁨days⁩ ago⁩:

  Sometimes when I’m really tired in the morning I get out of bed like this, it’s the path of leadt resistance.

• ⁨Comment⁩ on ⁨IT'S A TRAP⁩ ⁨⁨1⁩ ⁨week⁩ ago⁩:

  A practical application is for example in probability theory (or anywhere that deals with measures) such as this question:

  If we generate a random real number from 0 to 1, what is the probability that it is rational?

  Because we know that the continuum is so much larger in a sense than the set of rationals, we can answer this confidently and say the probability is zero, even though it is theoretically possible for us to get a rational number.

  Statistics deals with similar scenarios quite frequently, and without it we wouldn’t have the modern scientific method.

• ⁨Comment⁩ on ⁨IT'S A TRAP⁩ ⁨⁨1⁩ ⁨week⁩ ago⁩:

  There are infinitely many rational numbers between any two integers (or any two rationals), yet the rationals are still countable, so this reasoning doesn’t hold.

  The only simple intuition for the uncountability of the reals I know of is Cantor’s diagonal argument.

• ⁨Comment⁩ on ⁨Listen here, Little Dicky⁩ ⁨⁨3⁩ ⁨months⁩ ago⁩:

  It is just a definition, but it’s the only definition of the complex exponential function which is well behaved and is equal to the real variable function on the real line.

  Also, every identity about analytical functions on the real line also holds for the respective complex function (excluding things that require ordering). They should have probably explained it.