Fix ASI for Python in Set Theory

22

I don’t understand the question. You can’t just ‘assume’ that an impossible thing is possible as your starting point.

Like I said, it’s only possible for Python to check if a finite number of finite sets meet the omniscience principle for a finite number of two valued functions.

You can’t prove anything about an infinite set with an infinite number of two values functions by checking every case. That’s literally impossible. That’s what mathematical logic and proofs are for.

Let’s step back. What is your end goal? What are you trying to do?

23

The problem isn’t your disbelief in infinite computations

It’s that N needs to be a loop of its inclusion

Returns are needed from the first equations

x.index(i) needs to be counting set inclusion of other sets

Stuff like that
Whatcha got?

24

I believe in infinite computations just fine. I am a computational mathematician, and I’ve been writing proofs involving infinity for more than 15 years. The problem is not in my understanding of infinity.

The problem is that you don’t understand how programming works. You cannot write a loop that will iterate an infinite number of times and expect it to report a result back to you. That loop will never stop, definitionally.

  1. The term ‘loop of its inclusion’ is not a technical phrase in either mathematics or programming. What do you mean? You still can’t get a result from a loop that iterates an infinite number of times. You have to do the mathematical work to convert that ‘loop’ (actually whatever that loop represents) into a closed form that can be computed.

  2. Equations don’t return things in programming. Functions return things. But you still can’t check every two valued function that exists for an infinite set with a computer program.

  3. You can’t make an infinite set like that in Python.

Again - what are you trying to do? If you can articulate what you want Python to do, I can help you get Python to do it.

You can’t just type a version of those equations into Python and hope that it understands what you want. You need to break the problem into discrete, finite tasks that work towards your end goal. Computers are stupid and need exact, precise directions. If you tell them to do something infinitely, they will literally do it until the end of time. But by then you’ll be dead and the calculation still won’t be done.

25

Ok no returns needed
I’ll make a function for X

How do I count number of sets including sets

26

Consider, for example, the specific case of computing the sum of a p-series.

When p > 1, the infinite series with terms given by 1/n^p has a finite sum, and that sum is given by the Riemann zeta function. We can compute the value of that sum to an arbitrary precision by running a loop over a finite number of terms.

But this only works because we know mathematically that this series converges.

If we attempt this same trick with the harmonic series, we can compute the individual harmonic numbers, but we can never reach the actual sum of this series, as it does not exist.

There are plenty of problems we can express with infinities that computers simply can’t make statements about. We need to use mathematical logic to know what things computers can make statements about.

So we cannot verify that a property holds true for every member of an infinite set by empirical verification. We cannot, for example, empirically demonstrate that every member of an infinite set maps to 1 for a specific two valued function. To check every member of an infinite set would literally take an infinite amount of time.

In that case, we would have to logically deduce that every member of the infinite set necessarily has to return 1 for a specific two valued function.

The problem becomes even messier when you want to verify that every single possible two valued function defined on a specific infinite set follows the omniscience principle. We can’t empirically check an infinite number of functions against an infinite number of items. We would, literally, be doing the task for an infinite amount of time.

Instead, we have to use mathematical logic to state that the omniscience principle must hold due to how the infinite set was constructed.

Computers are great at finite computations. They are great at large volumes of finite computations. But they cannot do mathematical thinking for us. We have to do the heavy lifting of discretizing a problem, or converting the infinite into a finite representation or form so that it is actually computable.

So, what is it that you want the computer to do? Big picture here?

27

I want to solve for x and i

28

“Solve for x and i” and what sense?

I’m not seeing any way in which “solve for x and i” makes sense in the context of this paper.

Are you trying to generate a portion of the generic convergent sequence?

29

More like include it in itself equaling what was there before

Lol so much for infinite recursion though

30

I don’t know what that means for x and i, and I don’t see how the paper you linked does anything that can be described that way.

You can certainly make the computer do infinite recursion, but it will never return an answer because you literally ask it to recurse forever.

31

Mm using compliments

32

How does using compliments let one ‘solve for x and i’?

33

K = x | i
x = K^c | i

34

What is i?
What is x?
What is K?

I really don’t understand what you are trying to do.

35

Sorry I’m so short on explanations
I have a new version that’s stuck on a type error

#Amend
def p ():
 w = set()
 N = [w]
 i = [w]
 x = [w]
 o = 0
 for o in range(len(N)):
  w = set(w)
  N = N.append(w)
  i = i.append(w)
  x = x.append(w)
  o = o + 1
  return N
  if o == float('inf'):
   break
  def powerset(z):
   r = [[]]
   for y in z:
    n = [s + [y] for s in r]
    r.extend(n)
  return r
 i = powerset(i)
 x = powerset(x)
 def a ():
  N
 k = N.index(float('inf')) is set(x in 2 >= N | all(i) in a(x.index(i) >= x.index(i+1)))
 global X
 X = 0  
 while X <= 2:
  X = X + 1
  any(k) in X(p(k) is 0) or all(k) in X(p(k) is 1)
q=""
while True:
 i=11
 while i < 126:
   i= i + 1
   m = chr(i)
   p ()
   v = p()
   if v == 1:
    q = q + m
   elif v == 0:
    q = q
 if q == q + "":
  break
print (q)

What does the type error mean

36

Your new code addresses none of the places where you are treating a variable declared in one type as if it is a completely different type.

Honestly, I’d pitch this code and start over with a clear description of what you want to do. If you can’t describe your goal in words, you certainly can’t describe it in code.

1 Like
37

Could you explain please

38

Explaining will make you think that this code can be fixed. It can’t.

1 Like
39

I’m getting the impression that your IDE is looping infinitely

I don’t have that problem unless I’m in a government owned building

40

That makes no sense. The building you are in has no effect on how the code runs.

41

JeremyLT could you delete this thread? I need a fresh start. Honest.