/sci/ - Science & Math

>>12611034
Unfortunately this is the "best" "method" available.

>>12611034
write them above each other
add each diggit with it according counterpart
carry the ones
repeat untill you run out of memory

>>12611111
I see you know how to carry your 1s.

>>12611102
AHAHAAHAHAHAHHAAH

>>12611102
based as fuck

>>12611138
That proof is garbage. How can you subtract terms in a limit if you haven't even defined addition yet?

>>12611034
Begin with laws of identity.
>1. Assume reflexivity is true, x = x.
>2. Assume transivity is true, x = y and y = z implies x = z.
Now assume multiple objects exist, x, y, and z.
>3. Construct an ordered set to combine objects, e.g. (x*y), (x*z), (y*z)
>4. Assume this * operation is commutative, (x*y) = (y*x)
>5. Assume this * operation is associative ((x*y)*z) = (x*(y*z))
>6. Assume there is an identity element, e, such that (x*e) = x, i.e. this identity element leaves the element it modifies unchanged with combination
>7. Assume there exists an inverse element y, such that (x*y) = e
>8. Match these abstract, logical rules to reality
Define an object that exists, example, a flower. I call that an identity element. A flower is a flower. I now notice another flower. I combine the flowers into a bouquet.
>9. Quantify specific combination scheme as addition

>>12611171
They start with rational numbers (for which addition is defined), and define reals as a certain types of limits of sequences of rationals.

Also >>12611034 please have the courtesy to stick to starting one finitist brainlet thread at a time. You already have >>12607457 going. No one's gonna think better of you if you keep spamming the catalog .

>>12611225
That proof doesn't demonstrate the existence of addition for real numbers. It assumes you can add real numbers, and then proves that it's well-defined.
>Assume it's define, we show it's well-defined
Is not the same as
>We demonstrate an operation exists by which we can add real numbers

>>12611225
>certain types of limits of sequences of rationals
>limits

to the trash it goes

>>12611241
It shows a certain existing addition operation (defined previously on Cauchy equivalence classes) preserves such equivalence classes, therefore it is well-suited to be addition for real numbers.

>>12611034
It's impossible.

>>12611260
>to the trash it goes
As does this thread.
No contradictions means real numbers werk.

>>12611291
>No contradictions
Prove it.

>>12611291
Naïve set theory "worked" despite having a contradiction that Russell exposed long after such axioms were flippantly used for centuries.