An INFINITY of INFINITIES?
@redyellowblackdog (10629)
United States
November 18, 2008 7:43am CST
Yes, it is true.
Mathematics concluded a very long time ago there is an infinity of infinites! How?
Start with the proof there is infinity.
Q: Is there any integer to which the number 1 can not be added?
A: No, therefore there is no "largest number". Numbers stretch into infinity.
Q: Is there any integer other than zero to which there is not a reciprocal?
A: No, therefore there is an infinity between each of the integers. Let me explain.
Starting with #1 of the integers consecutively figure the reciprocals and plot them thusly. 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10 ......
Note that as the integer gets larger, the reciprocal gets smaller, but will never reach zero, no matter what. Therefore, there is an infinity of reciprocals between 0 and 1.
Q: Is there any number to which any integer can not be added?
A: No, therefore if we add the integer #1 to the orginal infinity of reciprocals we produce a second infinity beginning at the integer #2 that approaches #1. We can likewise add any integer, (there are an infinity of them!) to the original infinity of reciprocals to produce another infinity between two other integers.
Therefore, there are an infinity of infinities.
I say this is pretty darn neat and conceptually proves at least of the feasibility of a mult-verse as opposed to our usual concept of a universe.
What do you say?
1 person likes this
1 response
@James72 (26790)
• Australia
19 Nov 08
I have been waiting for this one RYBD but somehow missed it! 
I agree that it is an extremely interesting angle to consider. Even before the days of the concept of multi-verses being being put forward and debated, we were always taught that the Universe was infinite. But standard schooling on Astronomy in general never really went deep into the mathematical comparisons or validations like this. I most certainly agree in the feasibility of there being multiverses because year on year we are seeing further, sending probes further; and discovering more and more galaxies and other astral phenomena that was previously innaccessible to us.
This is also why I am watching the efforts with the Haldon Collider with great interest. If the universe we know currently is indeed made up mostly of dark matter; and this collider helps us to understand it's properties better; then anything is possible. It may not be in my own lifetime but I have no doubt in my mind that our known universe is proverbially but a speck of sand on a never ending beach and there are a multitude of unknowns that will become knowns in ways beyond anyone's current imagination!
I agree that it is an extremely interesting angle to consider. Even before the days of the concept of multi-verses being being put forward and debated, we were always taught that the Universe was infinite. But standard schooling on Astronomy in general never really went deep into the mathematical comparisons or validations like this. I most certainly agree in the feasibility of there being multiverses because year on year we are seeing further, sending probes further; and discovering more and more galaxies and other astral phenomena that was previously innaccessible to us.
This is also why I am watching the efforts with the Haldon Collider with great interest. If the universe we know currently is indeed made up mostly of dark matter; and this collider helps us to understand it's properties better; then anything is possible. It may not be in my own lifetime but I have no doubt in my mind that our known universe is proverbially but a speck of sand on a never ending beach and there are a multitude of unknowns that will become knowns in ways beyond anyone's current imagination!1 person likes this
@James72 (26790)
• Australia
19 Nov 08
I definitely remember wormholes in Star Trek, Stargate and many other sci-fi books and movies! And you think Einstein would have been looked at sideways? Imagine what the rest of the world would have thought of the ancient Mayans thousands of years ago if communication was more advanced betwenn countries back then!
I found this amusing and interesting exchange between people on a science forum that you may find of interest as well: https://www.scienceforums.net/forum/showthread.php?t=28774&page=4
And this one too is very interesting: http://www.earlham.edu/~peters/writing/infinity.htm
1 person likes this
@redyellowblackdog (10629)
• United States
20 Nov 08
Thanks, for the links. While reading them it occurred to me we are probably the geekiest guys on myLot.
1 person likes this
Heck, I don't understand 70% of any of it but it's interesting all the same! Only way to learn is to jump in the deep end!