Infinity…… Infinite? Or Finite?

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In order for infinity to exist does it require an initial starting point?

If there were a beginning point would that point also serve as the end making what appeared to be infinite now finite?

“Infinite or until you reach your point of origination”. “Possibly Infinity”.

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Does this passage from a textbook dealing with the concept of infinity handle your question?


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In mathematics, it is possible to have an infinite series of numbers which starts with one. But in practice, the idea of infinity cannot begin with one, or any other number. Infinity is not a mathematical concept. It cannot be counted. This one-sided "infinity" is what Hegel calls bad infinity. Engels deals with this question in his polemic with Dühring:

"But what of the contradiction of ‘the counted infinite numerical series’? We shall be in a position to examine it more closely a soon as Herr Dühring has performed the clever trick of counting it for us. When he has completed the task of counting from – &#8734; (minus infinity) to 0, let him come again. It is certainly obvious that, wherever he begins to count, he will leave behind him an infinite series and, with it, the task which he has to fulfil. Just let him invert his own infinite series 1+2+3+4…and try to count from the infinite end back to 1; it would obviously only be attempted by a man who has not the faintest understanding of what the problem is. Still more. When Herr Dühring asserts that the infinite series of lapsed time has been counted, he is thereby asserting that time has a beginning; for otherwise he would have been unable to start ‘counting’ at all. Once again, therefore, he smuggles into the argument, as a premise, what he has to prove. The idea of an infinite series which has been counted, in other words, the world-encompassing Dühringian Law of Determinate Number, is therefore a contradiction in adjecto, contains within itself a contradiction, and indeed an absurd contradiction.

"It is clear that an infinity which has an end but no beginning is neither more nor less infinite than one with a beginning but no end. The slightest dialectical insight should have told Herr Dühring that beginning and end necessarily belong together, like the North Pole and the South Pole, and that if the end is left out, the beginning just becomes the end—the one end which the series has; and vice versa. The whole deception would be impossible but for the mathematical usage of working with infinite series. Because in mathematics it is necessary to start from determinate, finite terms in order to reach the indeterminate, the infinite, all mathematical series, positive or negative, must start with 1, or they cannot be used for calculation. But the logical need of the mathematician is far from being a compulsory law for the real world."

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I think that model would work if a line goes in each direction for infinite from 0 like every (+)positive number has its (-)negative number, if any (+) numbers do not have (-) numbers please tell me so then i can know for sure.

The intuitive mind

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Isn't infinity actually a process?
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I dont think it is, although you have assumed that it is in all of your reasoning.

My thinking is as follows: In order for infinity to be real, it has to be unchanging since it contains all that is [unless your proceed to redefine "infinity, as you have redefined "nothing"].

Infinity is therefore not a process.

This can only be reconciled with observations from a standpoint of time as one of the dimentions... and that fits in very nicely not only with MM and SR, but other theories as well. So I would propose that for infinity to exist, it does not require an initial starting point.

Any agreement out there? It puts an end to the "zero" hypothesis (not yet a "theory," as it is devoid of any possible confirming experiment.)

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So I would propose that for infinity to exist, it does not require an initial starting point.

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I agree with that. Although you can have processes get infinite and therefore require a starting point, infininity not only does not need one, but it must not have one, otherwise no process could reach infinity from an arbitrary starting point.

However, I disagree that all theories must be verified experimentally ,in the case of first causes, which may not be mechanical in and don't tell me this can be proven in any way, to be true or false.

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What about a "Hypothotheory", a hypothesis which is proven by pre-existing proofs, maths, principles, and experiments?
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If such a thing exists, it is the Universe itself. It exists, without any proofs, maths [sic] or experiment. Why would it then be a "hypo-anything." It would simply "be."

The definition fits "existence," which is what we are all arguing about.

So we can at least agree that existence "is." This deflates "nothingness." Please, please, please look deeper at the implications of MM into the dimention of scale...

NB. in MM, Infinity is not distinct from the reciprocal of Infinity (1/infinity) if space is "infinite." This should immediately resolve a large number of the unanswered questions postulated previously in this forum.

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In order for infinity to exist does it require an initial starting point?

If there were a beginning point would that point also serve as the end making what appeared to be infinite now finite?

“Infinite or until you reach your point of origination”. “Possibly Infinity”.


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On the issue of (mathematical) infinity and wether and how it relates to physical reality, here is a paragraph of a book on this issue.
(Anti-Duhring / Dialectics of Nature; F. Engels)

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V.
PHILOSOPHY OF NATURE.
TIME AND SPACE
We now come to philosophy of nature. Here again Herr Dühring has every cause for dissatisfaction with his predecessors.


Natural philosophy "sank so low that it became an arid, spurious doggerel founded on ignorance", and "fell to the prostituted philosophistics of a Schelling and his like, rigging themselves out in the priesthood of the Absolute and hoodwinking the public". Fatigue has saved us from these "deformities"; but up to now it has only given place to "instability"; "and as far as the public at large is concerned, it is well known that the disappearance of a great charlatan is often only the opportunity for a lesser but commercially more experienced successor to put out again, under another signboard; the products of his predecessor". Natural scientists themselves feel little "inclination to make excursions into the realm of world-encompassing ideas", and consequently jump to "wild and hasty conclusions" in the theoretical sphere {D. Ph. 56-57}.

The need for deliverance is therefore urgent, and by a stroke of good luck Herr Dühring is at hand.
In order properly to appreciate the revelations which now follow on the development of the world in time and its limitations in space, we must turn back again to certain passages in "world schematism" {15}.

Infinity -- which Hegel calls bad infinity -- is attributed to being also in accordance with Hegel (Encyclopaedia, § 93), and then this infinity is investigated.


"The clearest form of an infinity which can be conceived without contradiction is the unlimited accumulation of numbers in a numerical series {18} ... As we can add yet another unit to any number, without ever exhausting the possibility of further numbers, so also to every state of being a further state succeeds, and infinity consists in the unlimited begetting of these states. This exactly conceived infinity has consequently only one single basic form with one single direction. For although it is immaterial to our thought whether or not it conceives an opposite direction in the accumulation of states, this retrogressing infinity is nevertheless only a rashly constructed thought-image. indeed, since this infinity would have to be traversed in reality in the reverse direction, it would in each of its states have an infinite succession of numbers behind itself. But this would involve the impermissible contradiction of a counted infinite numerical series, and so it is contrary to reason to postulate any second direction in infinity" {19}.

The first conclusion drawn from this conception of infinity is that the chain of causes and effects in the world must at some time have had a beginning:

"an infinite number of causes which assumedly already have lined up next to one another is inconceivable, just because it presupposes that the uncountable has been counted" {37}.

And thus a final cause is proved.
The second conclusion is


"the law of definite number: the accumulation of identities of any actual species of independent things is only conceivable as forming a definite number". Not only must the number of celestial bodies existing at any point of time be in itself definite, but so must also the total number of all, even the tiniest independent particles of matter existing in the world. This latter requisite is the real reason why no composition can be conceived without atoms. All actual division has always a definite limit, and must have it if the contradiction of the counted uncountable is to be avoided. For the same reason, not only must the number of the earth's revolutions round the sun up to the present time be a definite number, even though it cannot be stated, but all periodical processes of nature must have had some beginning, and all differentiation, all the multifariousness of nature which appears in succession must have its roots in one self-equal state. This state may, without involving a contradiction, have existed from eternity; but even this idea would be excluded if time in itself were composed of real parts and were not, on the contrary, merely arbitrarily divided up by our minds owing to the variety of conceivable possibilities. The case is quite different with the real, and in itself distinguished content of time; this real filling of time with distinguishable facts and the forms of being of this sphere belong, precisely because of their distinguishability, to the realm of the countable {64-65}. If we imagine a state in which no change occurs and which in its self-equality provides no differences of succession whatever, the more specialised idea of time transforms itself into the more general idea of being. What the accumulation of empty duration would mean is quite unimaginable {70}.

Thus far Herr Dühring, and he is not a little edified by the significance of these revelations. At first he hopes that they will "at least not be regarded as paltry truths" {64}; but later we find:

"Recall to your mind the extremely simple methods by which we helped forward the concepts of infinity and their critique to a hitherto unknown import... the elements of the universal conception of space and time, which have been given such simple form by the sharpening and deepening now effected" {427-28}.

We helped forward! The deepening and sharpening now effected! Who are "we", and when is this "now"? Who is deepening and sharpening?

"Thesis: The world has a beginning in time, and with regard to space is also limited. -- Proof: For if it is assumed that the world has no beginning in time, then an eternity must have elapsed up to every given point of time, and consequently an infinite series of successive states of things must have passed away in the world. The infinity of a series, however, consists precisely in this, that it can never be completed by means of a successive synthesis. Hence an infinite elapsed series of worlds is impossible, and consequently a beginning of the world is a necessary condition of its existence. And this was the first thing to be proved. -- With regard to the second, if the opposite is again assumed, then the world must be an infinite given total of co-existent things. Now we cannot conceive the dimensions of a quantum, which is not given within certain limits of an intuition, in any other way than by means of the synthesis of its parts, and can conceive the total of such a quantum only by means of a completed synthesis, or by the repeated addition of a unit to itself. Accordingly, to conceive the world, which fills all spaces, as a whole, the successive synthesis of the parts of an infinite world would have to be looked upon as completed; that is, an infinite time would have to be regarded as elapsed in the enumeration of all co-existing things. This is impossible. For this reason an infinite aggregate of actual things cannot be regarded as a given whole nor, therefore, as given at the same time. Hence it follows that the world is not infinite, as regards extension in space, but enclosed in limits. And this was the second thing" (to be proved).

These sentences are copied word for word from a well-known book which first