What are the two varieties of infinity and how do they differ?

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Discussion Overview

The discussion revolves around the concept of infinity, specifically exploring different varieties and degrees of infinity. Participants debate the nature of infinity, including its implications in mathematics and its relationship to the universe, touching on both theoretical and conceptual aspects.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants propose two varieties of infinity: illusory infinity, associated with endless multiplication of zero, and real infinity, linked to endless division of real numbers.
  • Others argue that there are many degrees of infinity, including countable and uncountable infinities, suggesting that the concept is more complex than just two varieties.
  • A participant mentions Cantor's work, indicating that there is an infinite hierarchy of infinities, which challenges the idea of limiting infinity to just two types.
  • Another viewpoint suggests that while there may be many infinities, only one type corresponds to the universe's design, emphasizing a preference for a rational and economical infinity over one that leads to chaos and entropy.
  • Some participants provide mathematical examples to illustrate different types of infinity, such as limits approaching zero, and discuss their implications in terms of greater or lesser infinities.
  • There is a challenge to the notion that two infinities can be compared meaningfully, as some argue that if two values can be compared, they cannot be considered infinite.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the nature and classification of infinity. Multiple competing views remain, with some advocating for a limited perspective of infinity while others support a broader understanding that includes various degrees and types.

Contextual Notes

Participants express differing assumptions about the definitions and implications of infinity, with some relying on mathematical frameworks while others approach the topic from a philosophical or conceptual standpoint. The discussion highlights the complexity and nuance in understanding infinity, particularly in relation to the universe.

Michael F. Dmitriyev
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Exists two varieties of infinity.
1) Illusory infinity.
This infinity of the expansion. This process of the endless multiplying of the zero. If a zero is absolute that this process will not change nothing. The Zero will remain the Zero. For this reason interesting idea was invented. Absolute zero, in unknown effect, has ceased to be such in the some moment. Hereinafter this process had been applied to 3D space. But then it is necessary to acknowledge that it was received 3D number (? !) from absolute zero, for begining. Though such number is not possible to present, imagination of people has allowed to present product of one - continuously expanding 3D Space. For the scientific motivation of such model, it was happened to think up the ensemble of the props, which does not works. More exactly such a model leans onto illusion taken as reality.

2) Real infinity.
It present the result of the process of endless dividing of any real number. This is infinity of reduction of the source value.
Any a difference from absolute zero is endless. For this reason initial number can be as please small. The single necessities this existence of the absolute zero and such zero exists.
This infinity is real.

When considering these two varieties of infinity, for the reason buildings of such object as the universe, advantages of the second one is obvious with all standpoint. Though a compare the illusion with reality there is no point.
So. Infinity is directed on inward, to absolute zero, but not on outward, to absurd.

God does not allow the mistake unlike people.
 
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Only two?
 
Originally posted by Ben-CS
Only two?
Only one, indeed.
 
There are many degrees of infinity.

Im sure you know about countable and uncountable infinities for a start.
 
Originally posted by plus
There are many degrees of infinity.

Im sure you know about countable and uncountable infinities for a start.
Only one infinity is realized in the universe. This infinity is directed to absolute zero. This is my point. Except this one , I have considered the infinity accepted as reality on today. You may offer the other infinity which approaches on this role more than offered by me, on your opinion, and we can discuss this. But, agree, it is no reason to reduce this important question to discussion of the whole set of infinity.
 
Cantor actually showed that there is an infinite hierarchy of infinities. At least there is a countable infinity of different infinities.
 
Originally posted by ahrkron
Cantor actually showed that there is an infinite hierarchy of infinities. At least there is a countable infinity of different infinities.
You are right, ahrkron. However, on the some sign, we can select an infinity which closer corresponds to the designs of universe . On this sign an infinity of expansion is very distant off optimum for universe realization . On my glance it is straight opposite on reality.
 
Which infinity do you think corresponds to the 'infinity which closer corresponds to the designs of universe', and why is this so?

Simply by considering the borel sets and the sets of borel sets and the sets of sets of borel sets should show you that thestack of infinities are realized within the universe.
 
Originally posted by plus
Which infinity do you think corresponds to the 'infinity which closer corresponds to the designs of universe', and why is this so?

Simply by considering the borel sets and the sets of borel sets and the sets of sets of borel sets should show you that thestack of infinities are realized within the universe.

The Universe it is one object as integer. In ditto time it contains the endless ensemble of other objects and their combinations which are an objects also, i.e. it is a complex system. Within such a system can be realized the endless number of infinity. But one object can have only one inherent infinity defining its existence. The Universe too.
The one which has been directed on a proper goal or absoluteness, is rational, economical, is capable to develop and it is beautiful, at least. We can observe and explain it.
Unlike the other one which is
- profligate extraordinarily;
- overblown on enormous size;
- continues the senselessly expansion;
- prone at self-destruction;
Such universe is not capable to develop. Entropy is a straight opposition to evolution.
I prefer the first of two.

BTW, entropy can be only local and it is a necessary part of evolution.
We can observe it graphically in the surrounding world.
 
  • #10
there are different types of infinity. Some are greater than others.
For example

lim (x->0)1/x = infinity1

lim (x->0)1/5x = infinity2

the second equation goes to infinity faster than the first, so subtracting them will not equal zero. The infinity that includes all the real numbers is aleph-1, (might be wrong I haven't had number theory in a while).
But I do remember that there are definitely different types of infinity.
 
  • #11
Originally posted by schwarzchildradius
there are different types of infinity. Some are greater than others.
For example

lim (x->0)1/x = infinity1

lim (x->0)1/5x = infinity2

the second equation goes to infinity faster than the first, so subtracting them will not equal zero. The infinity that includes all the real numbers is aleph-1, (might be wrong I haven't had number theory in a while).
But I do remember that there are definitely different types of infinity.
If you may compare two values by subtractions, for instance, then these values are not infinity.
 

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