... volume. If you then gent a similar cylinder at twice the height is it the same infinite volume or different. Could you have an infinte number of infinities?
Responses (1)
Infinity is A NUMBER larger than you can measure. If you only have a twelve inch ruler then thirteen inches is infinity.
Bazillions of people assume that infinity is a number without limit. Mathematicians use both definitions, assuming that their fellows know what they mean, and that works well enough as long as they are not talking about reality.
In reality the longest ruler we have is the Earth's orbit. By triangulation we can accurately measure the distance to stars up to about 3200 light years away. Beyond that is infinity. That is why the size estimates of stars more than 3200 LY distant are so uncertain.
Let's consider another example: Are there an infinite number of stars? The number is obviously bigger than anybody can count, so by one definition we do. But we can easily disprove the idea that the number of stars has no limit. If there were no limit to the number of stars then every line of sight would end on a star and space would be bright. Space is dark. Therefore there is a limit to the number of stars.
Most people never even consider the definitions of the words they use. They might know what they are talking about, but they don't know what they are saying.
Aren't you being a bit simplistic.If you consider 1/n this approaches zero as n increases and becomes zero when n is is infinite. So in my question we could consider the ratio of unit volume to the infinite volume of the infinitely extended cylinder. If the cylinder was then increased in height the initial volume would increase but the final ratio would be zero-so does this mean the value of the divisor has increased?
I am not sure what your point is. The dual definition of 'infinity' allows an awful lot of word play.
You keep talking about wordplay but I am not arguing semantically. It seems a perfectly reasonable argument to me that 2/n will be larger than 1/n for any number. Therefore to get 2/n to equal zero you need a larger number than that to make 1/n equal zero. By extension you can then argue for an infinite number of infinities. That is my reasoning and all I was asking was for a mathematical refutation (or agreement). Am I just being mathematically naive?
No, a lot of people have argued about this subject. In the end you conclude that math is valid only when it describes reality, and n/0 is not a true example of reality. It is a word game. The only known example of actual n/0 is sonoluminescence. We think. Even there it never actually gets to zero, but in theory it could.
Please explain -what is infinity if not a mathematical concept?