Infinity +1

[AntiChrist]

Does an infinite thing have to be constantly expanding to be infinite?

 

(Like the universe we exist in)

[◊ Weezer ◊]

The first thought that came to my mind is that it can't get any bigger than infinite. 

[AntiChrist]

8 minutes ago, Weezer said:

The first thought that came to my mind is that it can't get any bigger than infinite. 

Does subtracting (-1) from infinity cause an infinite number of nine's? (That must continually expand forever in nine's?)

 

Is that the correct idea?

[◊ Weezer ◊]

I have no idea.  Math is not my "cup of tea."

[Wertbag]

2 hours ago, EnaUnited said:

Is that the correct idea?

Not to my mind.  Infinity is not a number, it is a concept.  It is the thought of something that is uncountable, something without end.  You can't do maths on a concept.

The only thing I can think of that might be infinite would be matter, with the idea it can never be created or destroyed, so all the matter we have has existed as long as the universe has.

 

5 hours ago, EnaUnited said:

Does an infinite thing have to be constantly expanding to be infinite?

No, a "thing" is too vague, the only "thing" for which expansion is known is the universe, but even then we can't say it is infinite.  We simply don't know what it is expanding into and whether there is any kind of limit.

[pantheory]

On 6/13/2020 at 8:36 PM, EnaUnited said:

Does an infinite thing have to be constantly expanding to be infinite?

 

(Like the universe we exist in)

 

Infinity is a concept, not necessarily a reality. In certain aspects of mathematics the concept of infinity is used to solve problems that would be much more difficult to solve without it. In the mathematics of calculus, for instance, the concept of an infinite limit is used in both differential and integral calculus. Calculus is used in many aspects of both science and engineering.

 

In mathematics, infinity can be graded as to its relative size compared to another infinity if its rate of growth is at a faster rate of growth or expansion. But no, infinity does not have to expand to be infinite.  Most scientists believe that the universe of matter is not infinite, but most also believe that the universe of space is infinite. But others believe that space is no more than the distance between matter and the volume matter occupies. If this is correct then where matter ends in volume, if it does, then space also ends. Rene Decarte, the famous French philosopher and scientist, believed that space is best defined and described as an extension of matter.

 

In any case there may be no such thing as infinity in reality, just an indispensable mathematical concept. If so then everything has a limit to it. Of course the Big Bang model (BB) of the universe today is accepted by maybe 98% of astronomers and theorists, and even a greater percentage believe the universe is expanding. But this is not fact, it remains theory. The evidence for this expansion is that there is a direct correlation between the redshift of galaxies to their distance from us first discovered by Edwin Hubble.  But this is not certain evidence for an expanding universe. There are many other hypothesis explaining redshifts other than an expanding universe. Hubble himself believed that the universe was not expanding and that there was another reason for galactic redshifts other than an expanding universe. Here is a quote concerning his beliefs:

 

"Hubble believed that his count data gave a more reasonable result concerning spatial curvature if the redshift correction was made assuming no recession. To the very end of his writings, he maintained this position, favoring (or at the very least keeping open) the model where no true expansion exists, and therefore that the redshift "represents a hitherto unrecognized principle of nature.

 

There are other factors also that make most scientist believe the universe is expanding, but there is also much evidence against its expansion. In an expanding universe, for instance, galaxies in the past should have been closer together. But no matter how far back in time they look, distances between galaxies appear to be the same or even greater in the past. This is totally contrary to the BB and an expanding universe. There are a great many other reasons to conclude that the BB is wrong and that the universe is not expanding. I am a cosmologist and an associate and I wrote and published a pier reviewed paper on the almost countless problems with the Big Bang model which you can see in a link below. Probably the only reason why the BB still remains the preferred cosmology is that cosmologists do not know of any other model that they believe meets all their requirements other than the BB model. But maybe 3 to 10 years from now when the James Webb space telescope is up and properly placed, it will be able to see much farther than the Hubble telescope or most any ground based scopes including radio telescopes. After that, there may be many reasons why the BB model will seriously begin to fall out of favor and a replacement non-expanding universe hypothesis may then be considered.

 

https://en.wikipedia.org/wiki/Infinity

https://en.wikipedia.org/wiki/Edwin_Hubble

https://www.prnewswire.com/news-releases/problems-with-big-bang-cosmology-300107094.html

 

 

[pantheory]

On 6/13/2020 at 11:48 PM, EnaUnited said:

Does subtracting (-1) from infinity cause an infinite number of nine's? (That must continually expand forever in nine's?)

 

Is that the correct idea?

 

No. Infinity is not a round number. In mathematics infinity minus one would still be infinity, just a lesser degree of it.  Infinity minus any number would still be infinity. Just consider that infinity is an almost indispensable mathematical concept, not necessarily a part of reality.

[♦ Fuego ♦]

[Justus]

On 6/13/2020 at 10:36 PM, EnaUnited said:

Does an infinite thing have to be constantly expanding to be infinite?

 

(Like the universe we exist in)

There is no 'infinite'  monster except in the heads of theoretical philosophers who know a finite object which is expanding is still a finite object whether it expands or not.

[midniterider]

Is a theoretical philosopher one that doesn't really exist?

[pantheory]

On 6/20/2020 at 8:52 AM, Justus said:

There is no 'infinite'  monster except in the heads of theoretical philosophers who know a finite object which is expanding is still a finite object whether it expands or not.

 

Justus,

 

I gave you an "I like" above because I agreed with what you said. But remember that God is also supposed to be infinite, and I think that the belief in infinity is essential to the belief in God. The concept of infinity including the belief in a god of any kind seems to be necessary for the multitudes, most of which have minimal educations or understandings of scientific reality. 

[pantheory]

17 hours ago, midniterider said:

 Is a theoretical philosopher one that doesn't really exist?

---

 

“A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.”  Max Planck

 

Unfortunately your quote has a lot of truth to it. But occasionally these scientific truths are not new, just unknown, discounted, bypassed, or believed to be disproved. But in time all truths will come to the surface and float in the sea of other truths. All in time will be recognized at least from one perspective.

 

I realize you were responding to Justus concerning his wording "theoretical philosopher, whatever that is? "

 

As to your posting and Justus' theoretical philosopher, IMO all philosophies and theories are perspectives of reality, not reality themselves. Some of them have their basis in truths. But no philosophy or theory is ultimately true as a whole, but many are based upon numerous truths.

 

As to religions and their belief in an infinite God, the value to them is unrelated to their beliefs IMO. Many do good charitable works around the world, create goodwill within the community, and many have moral-value teachings which can lead to a better life for individuals and their society as a whole, whether or not one believes in their God or religious teachings. Religions and their aggressive followers, however,  have also been the perpetrators of many wars in the name of their religion and countless psychological damage to some of their believers.

[pantheory]

On 6/18/2020 at 4:41 PM, Fuego said:

 

 

Pretty cool. I see a Crusader' cross in the lower left hand corner. After finally losing the holy land in the second and third crusades, the sailors of the third Crusade might have realized his religion was a failed model

[disillusioned]

On 6/18/2020 at 3:19 PM, pantheory said:

 

No. Infinity is not a round number. In mathematics infinity minus one would still be infinity, just a lesser degree of it.  Infinity minus any number would still be infinity. Just consider that infinity is an almost indispensable mathematical concept, not necessarily a part of reality.

 

The bolded is not quite correct. I suspect this is because you're trying to simplify things,  but I'd like to go a step further in the interest of being thorough.

 

There are degrees of infinity, but subtracting a "normal" number from infinity is simply not an option, because infinity is not a "normal" number, and subtraction is an operation on a field of (usually) "normal" numbers (the natural numbers, say). I think it's best to think of infinity as being a measure of the cardinality (the number of elements in) a set. The set {1, 2, 3} has cardinality 3. The set of natural numbers (ie, {1, 2, 3, ...}) is defined in such a way that it has no upper bound. Hence, it has infinite cardinality. (This is not to say that having no upper bound is necessary for infinite cardinality. It isn't.)

 

Here's the point, for now: if we delete a number from the set of natural numbers, the cardinality does not change at all. We can actually do even better that this. If we consider only the even numbers (ie, delete half of the natural numbers) we can prove fairly easily that the cardinality of this new set is exactly the same as the cardinality of all the natural numbers. In layman's terms, this means that there are exactly as many even numbers as there are even and odd numbers combined. This is an interesting example of why it simply makes no sense to talk of adding or subtracting, in the "normal" sense, to infinity. It isn't a "normal" number.

 

Having said this, there are sets which have greater cardinality than the natural numbers. Such sets are said to be "uncountably infinite". The set of real numbers is probably the best example. Proving that the real numbers is uncountable was a major accomplishment of Georg Cantor. Now the really crazy thing: it is possible to prove that the subset of real numbers between zero and one has exactly the same cardinality as all the real numbers. Again, in layman's terms, this means that there are exactly as many numbers between zero and one as there are numbers in general. It is an open question whether or not there are sets which have cardinality between that of the natural numbers and that of the reals. The proposition that there are no such sets is called the "Continuum Hypothesis", and it is an open question in mathematics whether or not it is correct.

[Bhim]

@disillusioned if I remember intro analysis correctly (which I dropped after a week to take differential geometry instead...), if there is a mapping between an arbitrary set A and the natural numbers N which has a one-to-one correspondence - i.e. it is one-to-one and onto - then set A has the same cardinality as N. Essentially, you have to be able to label every a in A with unique indices 1...n for some n in N. Is that about right?

[Bhim]

On 6/14/2020 at 1:48 AM, EnaUnited said:

Does subtracting (-1) from infinity cause an infinite number of nine's? (That must continually expand forever in nine's?)

 

Is that the correct idea?

 

Fun fact: in general, real numbers don't have a unique decimal expansion. The number 0.999... (infinitely repeating 9's) is exactly equal to 1. It is not "approximately" equal to 1. The two are the same number, represented in two different ways. The subset of real numbers which are rational (i.e. they can be represented as a ratio of integers) have unique decimal representations. But the real numbers do not generally have this property.

[pantheory]

2 hours ago, disillusioned said:

 

The bolded is not quite correct. I suspect this is because you're trying to simplify things,  but I'd like to go a step further in the interest of being thorough.

 

There are degrees of infinity, but subtracting a "normal" number from infinity is simply not an option, because infinity is not a "normal" numbe

 

Yes. If I thought posting a related  link involving mathematical symbols I would have chosen this link concerning types of infinity in mathematics. Calculus I

 

https://tutorial.math.lamar.edu/classes/calcI/typesofinfinity.aspx

 

For positive infinity, infinity plus or minus any number equals infinity; Infinity plus infinity equals infinity.  Any positive natural number multiplied times infinity equals infinity. Positive infinity multiplied time positive infinity equals infinity  Infinity divided by a positive number equals infinity.  For negative infinity algebraic rules apply.  in division infinity (countable) divided by infinity (uncountable) equals zero. Infinity (uncountable) divided by infinity (countable) equals infinity.

 

All of this is likely to be viewed as gibberish for most people unless they understand and  have need to do the related mathematics.

 

 

 

 

[pantheory]

36 minutes ago, Bhim said:

 

Fun fact: in general, real numbers don't have a unique decimal expansion. The number 0.999... (infinitely repeating 9's) is exactly equal to 1. It is not "approximately" equal to 1. The two are the same number, represented in two different ways. The subset of real numbers which are rational (i.e. they can be represented as a ratio of integers) have unique decimal representations. But the real numbers do not generally have this property.

 

Yes, the example that I thought of posting was:  the sum of an infinite series  of fractions of 1 with successive divisions by 2:    1/2 + 1/4 + 1/8 + 1/16 .....etc.. also equals exactly 1.

[disillusioned]

1 hour ago, Bhim said:

@disillusioned if I remember intro analysis correctly (which I dropped after a week to take differential geometry instead...), if there is a mapping between an arbitrary set A and the natural numbers N which has a one-to-one correspondence - i.e. it is one-to-one and onto - then set A has the same cardinality as N. Essentially, you have to be able to label every a in A with unique indices 1...n for some n in N. Is that about right?

 

Yes, that's right. Establish a bijection between the two sets (a one-to-one and onto function, both injective and surjective) and you've shown that A and N have the same cardinality.

 

For the even numbers and the naturals, the function is just f(x)=2x. It's easy to show that this is a bijection, which is what I meant when I said it was easy to prove that the evens have the same cardinality as the naturals.

[disillusioned]

1 hour ago, pantheory said:

 

Yes. If I thought posting a related  link involving mathematical symbols I would have chosen this link concerning types of infinity in mathematics. Calculus I

 

https://tutorial.math.lamar.edu/classes/calcI/typesofinfinity.aspx

 

For positive infinity, infinity plus or minus any number equals infinity; Infinity plus infinity equals infinity.  Any positive natural number multiplied times infinity equals infinity. Positive infinity multiplied time positive infinity equals infinity  Infinity divided by a positive number equals infinity.  For negative infinity algebraic rules apply.  in division infinity (countable) divided by infinity (uncountable) equals zero. Infinity (uncountable) divided by infinity (countable) equals infinity.

 

All of this is likely to be viewed as gibberish for most people unless they understand and  have need to do the related mathematics.

 

 

All good. These are inherently tricky things to try to explain in the vernacular of the general public.

[pantheory]

1 hour ago, disillusioned said:

 

All good. These are inherently tricky things to try to explain in the vernacular of the general public.

 

I agree. That's why I chose not to post any link in the first place. In our forum we express our opinions or try to explain things, not post equations or links that would be gibberish to most readers unless appropriate.

[Bhim]

1 hour ago, pantheory said:

 

I agree. That's why I chose not to post any link in the first place. In our forum we express our opinions or try to explain things, not post equations or links that would be gibberish to most readers unless appropriate.

 

I understand your concern, but actually I think that posting equations might be the appropriate solution here. I have found that a reasonable number of people can rise to an intellectual challenge when it is presented. Perhaps @webmdave could look into having the forums support a LaTeX plugin, so that we can more easily post equations?

[pantheory]

33 minutes ago, Bhim said:

 

I understand your concern, but actually I think that posting equations might be the appropriate solution here. I have found that a reasonable number of people can rise to an intellectual challenge when it is presented. Perhaps @webmdave could look into having the forums support a LaTeX plugin, so that we can more easily post equations?

 

I understand that some can understand algebraic equations, but IMO the readership in general here would not be interested in equations requiring LaTeX. But if they agree with such a plug -in then great  

[disillusioned]

On 6/21/2020 at 9:39 PM, Bhim said:

 

I understand your concern, but actually I think that posting equations might be the appropriate solution here. I have found that a reasonable number of people can rise to an intellectual challenge when it is presented. Perhaps @webmdave could look into having the forums support a LaTeX plugin, so that we can more easily post equations?

 

I don't mind this idea, and I'm happy to post equations here, or elsewhere as necessary. But I can't help but feel that those who would benefit from the equations are probably the same people who would be likely to seek out that information for themselves if they felt it was necessary for their understanding. Or at least ask follow-up questions. And those who wouldn't benefit, wouldn't benefit either way.

 

 

[Wertbag]

Atheists don't solve exponential equations because they don't believe in higher powers.