1 in an infinity
- Antonio Terra
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Re: 1 in an infinity
I am not an expert, but my understanding is that one divided by infinite would give you a possibility qual to the "lowest number different from zero".
SInce such number theoretically does not exist, the calculation would be impossible, and would result in something like:
0,0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000...
A repeting decimal with no real number that we can see at the end. It is so close to zero that you could do a numerical aproximation that is closer to reality than any other numerical aproximation (excluding others that have X,0000... or X,9999...).
However, i'm not sure if this scenario is logicaly possible even within the realm of hipothesis.
- Mark1955
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Re: 1 in an infinity
From a more serious persective, infinity is not a number it is a philosophical concept [otherwise you could have infinity plus 1]. We do maths with numbers and philosophy with concepts. Would you try to enumerate empathy.
- Mark1955
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Re: 1 in an infinity
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Re: 1 in an infinity
And yet we do indeed do maths with infinities. See, for example, Cantor sets. We do useful maths with all sorts of strange concepts, like the apparently non-existent square-roots of negative numbers.Mark1955 wrote:...infinity is not a number it is a philosophical concept [otherwise you could have infinity plus 1]. We do maths with numbers and philosophy with concepts...
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Re: 1 in an infinity
To answer my own follow-up question:Steve3007 wrote:I'm going to go with zero. Is there a follow-up question?
I have one: If you randomly pick one of the infinite set of all real numbers what is the probability that it will also be one of the infinite set of natural numbers or integers? What is the probability that it will be one of the infinite set of even numbers?
Tending to zero.
The infinite set of all real numbers is infinitely bigger than the infinite set of integers. The infinite set of integers is the same size as the infinite set of even numbers.
- Antonio Terra
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Re: 1 in an infinity
There are many who don't quite agree with Cantor, but he is indeed accepted by most mathematicians.Steve3007 wrote: ↑May 9th, 2019, 10:40 amTo answer my own follow-up question:Steve3007 wrote:I'm going to go with zero. Is there a follow-up question?
I have one: If you randomly pick one of the infinite set of all real numbers what is the probability that it will also be one of the infinite set of natural numbers or integers? What is the probability that it will be one of the infinite set of even numbers?
Tending to zero.
The infinite set of all real numbers is infinitely bigger than the infinite set of integers. The infinite set of integers is the same size as the infinite set of even numbers.
Don't you guys think that mathematicians need to deal with concepts, since numbers are all concepts?
- Mark1955
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Re: 1 in an infinity
Fair point, but infinity in a Cantor set just means don't stop doing this, it isn't a thing so much as an instruction. By comparison the square roots of negative numbers have values and can be and are manipulated accordingly. That one 'rule' of maths says they can't exist just suggets that the 'rules' aren't alwasy as simple as they seem; or more to the point, as we'd prefer them to be.Steve3007 wrote: ↑May 9th, 2019, 10:33 amAnd yet we do indeed do maths with infinities. See, for example, Cantor sets. We do useful maths with all sorts of strange concepts, like the apparently non-existent square-roots of negative numbers.Mark1955 wrote:...infinity is not a number it is a philosophical concept [otherwise you could have infinity plus 1]. We do maths with numbers and philosophy with concepts...
- sebam83
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Re: 1 in an infinity
2023/2024 Philosophy Books of the Month
Mark Victor Hansen, Relentless: Wisdom Behind the Incomparable Chicken Soup for the Soul
by Mitzi Perdue
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Rediscovering the Wisdom of Human Nature: How Civilization Destroys Happiness
by Chet Shupe
March 2023