# dividing infinities

something came up in one of the discussions here which i found strange.

there is the proposition that infinity/infinity= finite determinate.

how can this be possible. my take is it isnt infinite divided by infinite can only give an infinite number.

well, the set of all integers is twice as big as the set of all positive integers. so dividing all by positive should be 2, yeah?

Neither infinity nor infinitesimal by definition of it being 1"/"by an infinity is a definable number, so when that came up you should of probably said, you cannot perform a mathematical function on an infinity.

Infinity +1. infinity^infinity are all infinity. Even if that is a way to win an argument when you are 9.

Infinity/infinity is undefined as is all application of math that is a number on the concept of infinity, and I want to make this perfectly clear, even if James claims otherwise, or cardinality issues occur.

In standard mathematics, that is “indeterminate”, “insufficient information”.

You have to define a cardinality and a ratio before you can use standard mathematics with infinities and get an actual answer.

But if you merely know that you have two infinities being divided, you know that you have the opportunity for the result to be finite.

Zeno’s paradoxes are examples of divided infinities;
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.

The resolve of this, like all of the Zeno paradoxes, is that with each of the infinite number of segments getting smaller, it takes a similar smaller amount of time for each of the infinite segments to be traversed. So even though there are an infinite number of segments, the average time for each segment is infinitesimal.

Infinitesimal * infinite == infinite / infinite = “some finite number, but indeterminate as to what that number would be”.

y6ou can axiomatically propose that it equals something…

this would suggest that one infinity is equal to another, smaller and larger infinity is an oxymoron, i would prefer denser as a better alternative.

if this is not the case then its like trying to divide 0/0=1?

No, it merely suggests that neither is infinitely greater than the other. No cardinality was defined to say otherwise.

Semantics. One variable might reach infinity twice as fast as the other, in which case one variable is always twice the other (yielding “2” as the ratio). There is insufficient information to know the details.

reach infinity twice as fast? infinity cannot be reached. explain.

“reach toward infinity”… “the limit as x goes toward infinity”… you know what I meant.

there is the set of numbers they are infinite… 1,2,3,4,5…

there is the set of even numbers they are infinite 2,4,6,8…

one is said to be bigger than the other but i will show you why this is not the case.

normally when talking about quantities this is done by taking a determined set. e.g numbers 1-100. this would give the results

100 for the first

50 for the second

one can be said to be twice as “big” in terms of the number of sets present in the infinity.

this is misleading because as soon as a division is set it ceases to be infinite, infinity does not have a determined set so whether one has more of something in a set is irrelevant since the set is never determined one can only speak about denser infinities, not about larger ones.

if this is what you call opportunity to find one its alright but this can only be achieved by determining the set that if it is done destroys the infinity.

i would also argue the following if we look at infinites based on there ultimate value and not on the sets it contains, we will see that no infinity can be larger or smaller than he other.

for example: set of integers 1,2,3,4…

``````                set of even 2,4
``````

that one is “larger” denser than the other, however 4=4 when it comes to value they are still equal to the other.

if you the say what if integers set ends in 5? well it doesnt because its infinite, to make it determinate would destroy the notion of infinity.

one could say one is reached twice as fast… this is a perception being mislead. since they both will reach 6 at the same time. only that one has to go through more sets than the other.

perhaps it would help to think of a infinite set of numbers as a wave and think in terms of frequency…

Er no it would help to think of a wave as having infinite ability to have any affect on something, that is vanishingly small as distance increases to the limit.

Best thing to do is think of infinity as a physical thing as impossible according to the laws of thermodynamics. Leave what is cardinality beyond an infinity to pure maths, at the end of the day the decimals and the integers are both the same size, but one can be larger on the basis you can always add more decimal places to .37463764374632 and so on, something you can’t do to the fractions or indeed integers. Decimal places however do not mean something is physically larger by definition only a cardinality of sets says there are more unique numbers in the set of decimals, hence the integers are the same “size” as the fractions, and the decimals are “larger” than both. hyper reals extend this to having a set and cardinality that has some value beyond that, but they are purely conceptual.

surely space is infinite though…?

Whatever gave you that idea, best estimates claim the universe is at least 93 billion light years wide.

thats the range of mass i said space…

Contemporary physics/cosmology claims that “the universe” is only what they can see of it and whatever proceeded from the BB.

No that’s the range of space, space - time and mass are the same thing by equivalency in general relativity.

Where as Christianity claims that there are unseen forces at work that control the universe, but were we to question God we would be committing a sin. James of course science works on what scientists can see, why would it want to work on imaginary pixies that exist in the far flung regions of Q space. Science is not a religion, any more than philosophy is, the 3 distinct areas all have their uses as long as they don’t tread too hard on each others toes.