At my age, @mchambin, I am forgetting Mathematics faster than I am learning it, but isn't the proof something to do with factorials?
https://en.wikipedia.org/wiki/Euclid's_theorem
5! = 1x2x3x4x5 for instance. 120 IIRC. Now add 1. 121.
Divisible by 11. Also a prime number, but larger than 1,2,3,4,5 whether prime or not.
The fundamental Theorem of Arithmetic. All integers are expressible as the product of primes or are prime themselves. NO. I give up! I know my limits.
My recently completed read:
Amazingly good Maths book.
Another of my Mathematical Heroes, John Horton Conway:
Everybody knows the taxicab number, 1729, an early glimpse of modular forms:
https://en.wikipedia.org/wiki/Monstrous_moonshine
Who'd have thought 196,883 matters? The dimension in which The Monster exists? 🙂
https://en.wikipedia.org/wiki/Euclid's_theorem
5! = 1x2x3x4x5 for instance. 120 IIRC. Now add 1. 121.
Divisible by 11. Also a prime number, but larger than 1,2,3,4,5 whether prime or not.
The fundamental Theorem of Arithmetic. All integers are expressible as the product of primes or are prime themselves. NO. I give up! I know my limits.
My recently completed read:
Amazingly good Maths book.
Another of my Mathematical Heroes, John Horton Conway:
Everybody knows the taxicab number, 1729, an early glimpse of modular forms:
https://en.wikipedia.org/wiki/Monstrous_moonshine
Who'd have thought 196,883 matters? The dimension in which The Monster exists? 🙂
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Hoping to find one mentioned to me but failing. 😉 This one is vaguely related
https://en.wikipedia.org/wiki/0.999...
It's interesting to note there are actual proofs and some that aren't really. Reminds me of something I was told. Infinity - don't use the term. There are very distinct rules about manipulation involving it. I suppose this is because it a rather commonly used word and people might think it can be handled just like ordinary numbers.
LOL I can remember a simple one. The statement n+1 > n is clearly correct. I recollect I should say for all reals but a long time ago.
Coincidently, tonight's new episode of The Sky At Night (BBC4, 9.30pm) visits the facility.
I just about followed the proof by contradiction in this link:
https://prateekvjoshi.com/2015/01/17/how-do-we-know-that-there-are-infinitely-many-prime-numbers/
That'll do for me!
I do know where the largest known Prime Number lives.
https://mersenneforum.org/showthread.php?t=5591&page=117
I never do anything but lurk at the Mersenne Forum. I know when I am out of my depth.
These Mathematicians are severely clever.
https://mersenneforum.org/showthread.php?t=5591&page=117
I never do anything but lurk at the Mersenne Forum. I know when I am out of my depth.
These Mathematicians are severely clever.
Here's a pure maths discussion of primes. Note not proven crops up but some of the ideas can be use in a probability fashion. Notice the use of the word lim. It's not like saying that 0.99'9 = 1. More correctly the limit is 1. It will never = 1
https://t5k.org/notes/gaps.html
There are a number of interesting pages.
https://t5k.org/notes/gaps.html
There are a number of interesting pages.
Actually, I'd call this one, ONE! (= 1). I know this infinite Mathematical trick.
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An Infinite set of Mathematicians enter a Bar. 😕
The First one says I'll have a Pint.
The Second one says I'll have a half Pint.
The Third one says I'll have a quarter Pint.
The Fourth one says I''ll have an eighth Pint....
The barman is weary of simple Infinity problems. He knows the Solution.
"Look" he says, "I am serving up 2 Pints".
😛
The First one says I'll have a Pint.
The Second one says I'll have a half Pint.
The Third one says I'll have a quarter Pint.
The Fourth one says I''ll have an eighth Pint....
The barman is weary of simple Infinity problems. He knows the Solution.
"Look" he says, "I am serving up 2 Pints".
😛
There is a quick and smart way to calculate the area of the sphere surface.
How ?
I vaguely remember it was proved a tedious way in school.
How ?
I vaguely remember it was proved a tedious way in school.
Similar to infinities
https://www.mathscareers.org.uk/calculating-pi/
We learn that we can start to write down Pi (π) = 3.141592653589….. but that we can never finish it. Pi (π) goes on forever and has no repeating pattern to its digits – it is what is called an irrational number. In fact if you search long enough within the digits of Pi (π) you can find any number, including your birthday.
.
.
Now that you know how to calculate Pi (π), you could always try your hand at memorising the decimal places of Pi (π). The most recent record was created on Pi Day in 2019 by Google, who calculated Pi to 31.4 trillion decimal places!.
LOL I wonder how they know it's correct Certainly can't measure and check it.
Mathematical games.
https://mathworld.wolfram.com/PiFormulas.html
https://www.mathscareers.org.uk/calculating-pi/
We learn that we can start to write down Pi (π) = 3.141592653589….. but that we can never finish it. Pi (π) goes on forever and has no repeating pattern to its digits – it is what is called an irrational number. In fact if you search long enough within the digits of Pi (π) you can find any number, including your birthday.
.
.
Now that you know how to calculate Pi (π), you could always try your hand at memorising the decimal places of Pi (π). The most recent record was created on Pi Day in 2019 by Google, who calculated Pi to 31.4 trillion decimal places!.
LOL I wonder how they know it's correct Certainly can't measure and check it.
Mathematical games.
https://mathworld.wolfram.com/PiFormulas.html
There was this science fiction short story I read a long time ago.
Up in the Himalayas there were these monks who believed the task of humankind in the universe was to solve some number, but the solution was very hard to do by hand.
So, they called the local IBM guys and they got a computer installed.
On the way down, during the early evening, the IBM guys were chuckling about the monks... but, at one point, one of them looked up and saw the stars disappearing from the sky.
Up in the Himalayas there were these monks who believed the task of humankind in the universe was to solve some number, but the solution was very hard to do by hand.
So, they called the local IBM guys and they got a computer installed.
On the way down, during the early evening, the IBM guys were chuckling about the monks... but, at one point, one of them looked up and saw the stars disappearing from the sky.
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On how Einstein’s GR and QM differ by 120 orders of magnitude 👇
https://bigthink.com/hard-science/worst-prediction-science-energy-empty-space/
https://bigthink.com/hard-science/worst-prediction-science-energy-empty-space/
Your link suggests that the discrepancy may be due to the fact that the standard model assumes that there is no smallest unit of space.
If there is one, then this changes the calculations and the disagreement between cosmic and quantum energy can disappear.
I've written before that the minimum Planck length may be regarded as an individual pixel of a pixilated spacetime.
https://www.fnal.gov/pub/today/archive/archive_2013/today13-11-01_NutshellReadMore.html
In other words, spacetime may not be perfectly smooth, but rather made of incredibly small discrete units.
A spacetime pixel is so small that if you were to enlarge things so that it becomes the size of a grain of sand, then atoms would be as large as galaxies!
"A spacetime pixel is so small that if you were to enlarge things so that it becomes the size of a grain of sand, then atoms would be as large as galaxies!"
Recursive space time...
That also means that an atom in a superior space time frame would exist in googles of space times in the inferior frame.
Recursive space time...
That also means that an atom in a superior space time frame would exist in googles of space times in the inferior frame.
The Planck length (ℓP) is an extremely small unit of length. It is calculated from three physical constants: the speed of light, the Planck constant, and the gravitational constant. The length was established as a way to simplify many of the more fundamental equations — if you write down equations in Planck units, you can do away with many physical constants and not have to worry about dimensions. The Planck length does not have any precise physical significance, and it is a common misconception that it is the inherent pixel size of the universe.[1]
It is about 1.616255×10−35 m or about 10−20 times the size of a proton. It is one of the Planck units, defined by Max Planck. It is an important length for quantum gravity because it may be approximately the size of the smallest black holes.[2]
The speed of light is also one Planck length per Planck time.
It is about 1.616255×10−35 m or about 10−20 times the size of a proton. It is one of the Planck units, defined by Max Planck. It is an important length for quantum gravity because it may be approximately the size of the smallest black holes.[2]
The speed of light is also one Planck length per Planck time.