B Is Infinity a Prime Number: The Confusing Concept of Infinity Explained

[CaptainJonathanNorth]

Infinity is both a number and a concept. I asked my 10 year old niece what kind of number infinity might be and she said, "It's a composite number." But I want to think about weather infinity is a prime number?

Clearly if you divide infinity by any number, you get infinity.
Also if you divide any number by infinity you get zero. Not sure this helps any.
If infinity divided by any number is still infinity, then perhaps infinity is a prime number after all. Though certainly not a normal kind of prime number.

 

[FactChecker]

Infinity is not a number in the field of real numbers. ∞ - ∞ and ∞/∞ are clearly ambiguous and undefined. Even if it was, we would have to say that 2 * ∞ = ∞, so 2 would be a factor of ∞ and it would not be a prime number.

 

[CaptainJonathanNorth]

Infinity is not a number in the field of real numbers. ∞ - ∞ and ∞/∞ are clearly ambiguous and undefined. Even if it was, we would have to say that 2 * ∞ = ∞, so 2 would be a factor of ∞ and it would not be a prime number.

Fair enough. By the way how do I get a math keyboard? Infinity has about four(??) different sizes. The simplest infinity is the number of point on a line, then the number of points in a square area, then volumes in a cube, then all rational b-splines in three space. The largest infinity is the total number of all possible curves in space.

 

[PeroK]

Fair enough. By the way how do I get a math keyboard? Infinity has about four(??) different sizes. The simplest infinity is the number of point on a line, then the number of points in a square area, then volumes in a cube, then all rational b-splines in three space. The largest infinity is the total number of all possible curves in space.

Where are you getting this stuff from?

 

[CaptainJonathanNorth]

Godel Escher Bach, An Eternal Golden Braid, by Douglass Hofstadter

 

[CaptainJonathanNorth]

Some of it is original thought too.

 

[PeroK]

Godel Escher Bach, An Eternal Golden Braid, by Douglass Hofstadter

You must be missing something. The "smallest" infinite set is the whole numbers: $\lbrace 1, 2, 3, \dots \rbrace$, then the Real numbers (the set of points in a line). But, the set of points in an area or a volume is the same size as the set of points in a line.

Whether there is an infinite set of intermediate size between the whole numbers and the real numbers is the subject of the Continuum Hypothesis.

To get a larger set than the real numbers, you could consider the set of all real-valued functions (of a real variable). That's roughly equivalent to all "curves".

Each time you find a bigger set, you can create an even bigger one, so this sequence of sets of increasing infinite sizes goes on indefinitely.

 

[CaptainJonathanNorth]

Right. We know all that. I have a hard time with theoretical math, applied seems to work a lot better,. The problem with infinity is infinity :^) :^)! But let me tell you what I am working on, and why it might matter. Suppose you were on the inside of a perfect sphere. The inner surface was a mirror. You are a point at the center, what do you "see"?

 

[PeroK]

Right. We know all that. I have a hard time with theoretical math, applied seems to work a lot better,. The problem with infinity is infinity :^) :^)! But let me tell you what I am working on, and why it might matter. Suppose you were on the inside of a perfect sphere. The inner surface was a mirror. You are a point at the center, what do you "see"?

Is there a light bulb somewhere?

 

[CaptainJonathanNorth]

No. There is a sensor.

 

[CaptainJonathanNorth]

Think of it as a spherical CCD

 

[CaptainJonathanNorth]

O.K. I get it, yes, there is a light source, somewhere outside the sphere, and there is a pinhole in the sphere which a photon can come through.

 

[PeroK]

No. There is a sensor.

If there is no light, then you won't see anything.

In any case, this has nothing to do with infinite sets.

 

[CaptainJonathanNorth]

Not so much infinite sets as infinitely flat surfaces, and such a flat surface has an infinite focal length.

 

[CaptainJonathanNorth]

Some of those images I sent are of the worlds flattest mirrors. The 12 inch, by 12 inch, by 1 inch thick, mirror is so flat, that if you projected a mathematically flat plane above it, parallel with the surface of the mirror. The lowest point on the mirror would be 10 to the minus nine inches apart from it.

 

[PeroK]

Some of those images I sent are of the worlds flattest mirrors. The 12 inch, by 12 inch, by 1 inch thick, mirror is so flat, that if you projected a mathematically flat plane above it, parallel with the surface of the mirror. The lowest point on the mirror would be 10 to the minus nine inches apart from it.

When physicists say "infinite focal length" or "point at infinity", they mean it much more loosely than the mathematical "infinite". "Infinite" focal length, for example, simply means that the light doesn't focus within any measurable distance.

 

[CaptainJonathanNorth]

These mirrors do some really amazing things.

 

[CaptainJonathanNorth]

For example, no matter how low an angle you look at the mirror, it never distorts or vanishes

 

[CaptainJonathanNorth]

I mean the image you see in the mirror never distorts or vanishes. Even when you are practically looking at the edge of the mirror, you can still see a complete image of your face.

 

[mfb]

Some of it is original thought too.

At your current level of education: Please don't. Most of that will be wrong, and then you get stuck in misconceptions.

The thread is drifting off into philosophy. As the original question is answered, I'll close the thread.