- Jan 17, 2005
- 44,905
- 1,259
- Country
- Canada
- Gender
- Male
- Faith
- Christian
- Marital Status
- Private
Well, if we stick a loaf of bread in that bracket, it would be 1. If that loaf represented the spiritual also reality, that 1 is not subject to the normal math we might apply to the object. If we stick an angel in there, it might not be easy to find either, when we try to add to it, or take away from it. It might be on the other side of the universe before you can do the math!The statement "The set {} is a proper subset of {{}}" is true, and under the usual interpretation of ZF, means that 0 < 1. What property of this universe am I using here?
Why is this concept of the five loaves so important to you? If I put five sandwiches on a plate, and then you eat one, and I add two while you're not looking, that doesn't mean that 5=6.
The spiritual added to the mix, with the physical results in a whole different kettle of fish. 5 certainly would equal 6 as soon as the first person took a loaf from the five, or second person, whatever. It is not established that more loaves were added. That is your opinion. Maybe it was all the same loaves that were involved, and they were replicated? Baby math just can't apply.
Well, if that limit exceeds what reality could deliver in this state universe, then we need to look at the limits of that present state conjecture.When I say that some sequence converges, I mean that it tends towards some limit. It is possible to prove the existence of the limit without knowing it's value. The concept of a nonconstructive proof is well-known.
Not really true, because what is in the sets has to represent a reality.No. Connectedness is a property of sets; it relates to the existence of paths between all points, where a path is defined via functions, which are defined via sets! No relation to the concrete universe at all!
The relation of what is in the one set to another has to represent something real as well. If we talk about the heavenly state, then what is real is different than the formulas, and relations, and possibilities we know today. Therefore, the math cannot hold it as you think.
Right, and it all depends on what is in the sets, and what y and x are to represent.The image of a function f is defined as the set of all y so that there exists an x so that f(x)=y. A function is a class of ordered pairs, and x and y themselves are defined in sets. Oh look, we're back to sets! Nothing to do at all with the concrete, physical universe.
But this universe state would have to be continuous for any of that to matter. You have no idea about that.Continuous has a precise definition, which involves limits, which can be defined in terms of the epsilon-delta definition that I used for 1/x before, which in turn can be reduced to... sets!
But we have already seen that the ZF concept depends on what all we are dealing with, and what exists. If you assume all the exists is what we normally run the numbers on, you are out in la la limbo land, dreaming in the dark.The function f(x)=x for all x in a given set S can be defined under ZF as the class of all sets {{z}, z} for all z in S. So for example, the identity function over the set of nonnegative integers is the class:
[ {{}}
{ {{}}, {}},
{ {{{}}}, {{}}},
...]
Doesn't look like there's any hidden 'universe' parameter there.
It means that math as we know it cannot be applied as a ruler, only as a servant! We tailor the math to the new realities, such as infinite speed potential, non physical only objects, etc etc.That doesn't mean that the mathematics is no longer true, it just means that the usage of the math to model the world is no longer correct.
In no way is that mickey mouse limiter, and stuck in the present mud foundation to be applied out of the fishbowl of the present state universe.The entire point is that ZF is a self-consistent model for mathematics, and that all of its theorems will still be true no matter what the state of the universe.
But it's application depends on reality, and a different reality requires something other than same old math.If it somehow works out that all the loaves of bread will never run out, then [/b]that doesn't mean math doesn't work, just that you can't apply math to it. Mathematics itself is unvarying and independent of the structure of reality.[/b]
Show me where one of the ten axioms of ZF states a property of the universe.
"
- Axiom of extensionality: Two sets are the same if and only if they have the same elements.
- Axiom of empty set: There is a set with no elements. We will use {} to denote this empty set.
- Axiom of pairing: If x, y are sets, then so is {x,y}, a set containing x and y as its only elements.
- Axiom of union: Every set has a union. That is, for any set xy whose elements are precisely the elements of the elements of x. there is a set
- Axiom of infinity: There exists a set x such that {} is in x and whenever y is in x, so is the union y U {y}.
- Axiom schema of separation (or subset axiom): Given any set and any proposition P(x), there is a subset of the original set containing precisely those elements x for which P(x) holds.
- Axiom schema of replacement: Given any set and any mapping, formally defined as a proposition P(x,y) where P(x,y) and P(x,z) implies y = z, there is a set containing precisely the images of the original set's elements.
- Axiom of power set: Every set has a power set. That is, for any set x there exists a set y, such that the elements of y are precisely the subsets of x.
- Axiom of regularity (or axiom of foundation): Every non-empty set x contains some element y such that x and y are disjoint sets.
- Axiom of choice: (Zermelo's version) Given a set x of mutually disjoint nonempty sets, there is a set y (a choice set for x) containing exactly one element from each member of x."
Right, and neither is the spiritual world. But if you want math to refect reality, it will have to deal with both, for the different state. Otherwise, it is meaningless.If you take one pile of hay and add it to another pile of hay, you just get one big pile. That doesn't mean that 1+1=1, though. It means that the physical world is not necessarily a model of mathematics.
They well may be the same loaves. Our concepts are too limited to deal in higher math. Baby math just goes so far.Well, if the fives we're talking about on 'the other side', whatever that may be, aren't the same fives, then of course they won't behave the same way. But the original fives still would.
A lot of man's so called wisdom deals in fantasy. The bits that happen to touch the real physical temporary world, as mickey mouse as they are in comparison with real state technology, and know how,Huh. Looks like that "absolute and utter literal foolishness, screaming lunacy, demented dreams, and silly stark raving madness" sure has done a lot, including create the computer you're using to post on these forums, the forums themselves, and pretty much everything you take for granted.
are better. But even they are childishly cavemanish in comparison to God's computers, and flying crafts, etc.
In no way will present math apply as the rule at all. It will only apply in it's place, as it can apply and does apply.My fundamental point here is that mathematics will always be self-consistent no matter what the state of the universe is.
Well, present numbers, and concepts of what to do with numbers, cannot model how heaven works, or the spiritual. They will have a place, but you are not yet in a position to know what that place will be. No matter how many brackets you pound out, or complicated equations you jot down, with present state math! Learn to live with your limitations.All that leaving the 'fishbowl' or whatever metaphor you want to use could do is change how you use it to model the world.
Upvote
0