Infinity, One and infinite infinities

[dwai]

 

[vonkrankenhaus]

Infinity cannot be "one", or "any".

If it was, it would be "Finite".

The infinite cannot grow or wither.

 

1 + Infinity = Infinity.

2 + Infinity = Infinity.

 

As many as he wants to add.

 

 

 

 

 

-VonKrankenhaus

[wandelaar]

Indeed there are many infinities, infinitely many. You don't need to be a guru to know that. A few minutes to consult the Wikipedia will do.

[Marblehead]

But it's all illusion so say the Buddhists.

 

[wandelaar]

If everything is an illusion, then nothing is an illusion. The concept of illusions only makes sense when you can point at something real by way of comparison.

[Nintendao]

If you can dream it, you can do it.

[Marblehead]

You ain't gonna' fly unassisted no matter how many times you dream of flying.

 

 

[Michael Sternbach]

There are indeed different levels of infinity.

 

https://www.businessinsider.com/the-different-sizes-of-infinity-2013-11

[wandelaar]

And that's just the beginning! After Cantor others discovered still other and/or more inclusive infinities. See:

 

 

[Marblehead]

Someone recently said that if your solution to an equation includes infinity you have made an error somewhere and you need go back and re-work you equation.

 

[wandelaar]

2 hours ago, Marblehead said:

Someone recently said that if your solution to an equation includes infinity you have made an error somewhere and you need go back and re-work you equation.

 

Depends on the problem. Most physical and technical quantities are finite, so when you find an infinite solution there is often an error involved. But this need not be the case! I leave it as an exercise for the reader to find a physical example where an infinite solution would be the correct answer.

[Marblehead]

Yeah, I suppose we could say that anything that cannot be defined has infinite possibilities.

 

[wandelaar]

Just now, Marblehead said:

Yeah, I suppose we could say that anything that cannot be defined has infinite possibilities.

 

Let me give you a hint. We will consider a certain experimental set up where a certain process takes a time T to finish depending on a certain angle α. Now it may happen that for α = 0 the process doesn't even start at all. In that case we should find that T =  + ∞ (seconds) for α = 0, and that would be the correct answer.

[Marblehead]

In that case I would take my ball and go home.

 

[wandelaar]

19 minutes ago, Marblehead said:

In that case I would take my ball and go home.

 

Very good! That's the example: a ball that rolls off an inclined plane till it hits some wall. T is the time it takes the ball to hit the wall. In case the plane is horizontal ( α = 0 ) than the ball will not even start rolling ( T =  + ∞ ). So then you could just as well take the ball and go home. 

[Lost in Translation]

5 hours ago, wandelaar said:

I leave it as an exercise for the reader to find a physical example where an infinite solution would be the correct answer.

 

x = 1 + 1/x

 

This describes the "golden ratio", roughly equal to 1.618.

[wandelaar]

Yes - that's an infinite solution in yet another sense :

 

https://codepen.io/pkra/full/xbgRNZ

[Marblehead]

I really don't like infinite solutions.  Too many choices to choose from.  Keep it simple.  Four multiple choice possibilities.

 

 

[moment]

On 11/11/2018 at 7:01 PM, dwai said:

 

 

Sounds like many of the late night coffeehouse discussions I used to have in college about 50 years ago.

[wandelaar]

@ Marblehead

 

Solutions can be infinite in many senses other than containing infinitely many possibilities. The golden ratio mentioned by LiT is a perfectly definite number. And the important number π has infinitely many digits. Besides - infinite processes are very important in (applied) mathematics! Keeping it simply by banishing infinite processes and/or numbers would paradoxically make things much more difficult.

[Marblehead]

I will just take your word for that.  But at least I can keep my check book balanced.

 

[Lost in Translation]

Let i = infinity

i

 

Let x = i

x = i

 

Since infinity is unlimited we can add anything to it and it will still be infinity. In this case we add infinity to itself.

 

x = i + x

 

Now we remove the common values from both sides of the equation, namely x.

 

0 = i

 

Infinity equals zero...

 

Spoiler

*** Mind Blown! *** 

Spoiler

 

 

 

[Marblehead]

Magic.