If a computer can't compute the number it doesn't

>>8813936
I knew it, 0.3 is bullshit

Computers can't compute rationals with infinite periodic expansion, therefore most of rationals don't exist, wildberger btfo

>>8813936
Is that le monke?

>>8814128
>implying there are more rationals with infinite expansion than without it

moron

>>8814132
if you're restricted to displaying your numbers in a specific base, then there are more rationals that continue indefinitely in that base than those that terminate in that base
if you don't know why this is then you're an imbecile or a child

>>8813936
>numbers
>existing
lol retard

>>8813936
Cantor would like to have a word

>>8813936
>>8814128

what does "compute" mean?
i think op wants to talk about computable numbers in the Turing "algorithmically computable" meaning.

if you can work with the representation "1/3" of 0.33333... or represent it as 0.1 in base 3, then then number at stake is computable

you can say this for any rational, so to make a point you'll try to construct more complicated numbers:

-not rational, but you can define them with an algebraic equation (polynomial) -> then you'll be using the equation as representation, work with that and get results with that. Those are called algebraic numbers, and this way there are still "computable"

-not algebraic, but defined with something usable by an algorithm to get info about them (for example the sequence of their decimals as far as you want it). pi and e are in this category. they're still computable in any decent definition of "computable", since you can work with the info you get by the algorithm. in this sense, the algorithm or its production is more or less your representation of the number you want to use.

-not definable with an algorithm: here the fun begins. look at the "computability" topic, starting with the Turing computability maybe, if you want to start making your mind on the subject.
check out the definition of Chaitin's (set of) constant(s) for definable-but-not-computable numbers
check out the different proofs of the Banach-Tarsky theorem/paradox, i remember one involving the "effective" construction of a non-measurable set of real numbers (with a choice axiom argument) leading to mindfucking results that remind me of the same feelings

>>8814139
Both are coutable you moron.

>>8814235
Some sets are more countable than others.

>>8813936
>what is symbolic computation

File: 1467985949564.jpg (93KB, 804x743px) Image search: [Google]

93KB, 804x743px

>mfw an ontologically uneducated plebeian is confusing existence and essence again