Is infinity A Number (listable infinity)
Debate Rounds (3)
which include Integers, natural numbers, whole numbers, rational numbers, irrational numbers, transcendental numbers, And then there are whole other sets which fall outside of the "Real Numbers" like infinitesimals, Imaginary numbers etc.
Now infinity Is a broad term, There are many different types of infinities, but each type of infinity does have an exact specific value. All listable infinities are the exact same value. There are the same number of natural numbers as there are integers (natural numbers are all positive whole numbers, not including zero. Integers are all whole numbers) And not only is its value definite, its also comparable. As its more than any real number and less than an unlistable infinity.
1. limitless or endless in space, extent, or size; impossible to measure or calculate.
Obviously as you have stated, you can have 1, 2, 3, 4, 5 with each of these number having an infinite amount of numbers going up to the next number. 1, 1.1, 1.2 etc etc etc. Each time you could add another 0. Infinity is not a number as it has no definitive value, we can give it the value though.
So, in the end, it's a principle.
If you look at some other non real numbers which are still numbers like imaginary numbers. there value is also impossible to define it is unknown is 1i is greater than or less than 2i and weather or not 1i = -1i since both 1i^2 and -1i^2 = -1.
Or infinitesimal numbers, the most popular of which famously known as the smallest number which is not zero. these are a type of surreal number because you know where they fit on the number line. except they aren't there. Right after zero but before anything els. Unfortunately no such spot accually exists so its not a real number.
Both of these have a set and defined value, it is just either unkown or unreachable. in the same way a listable infinity is a number.
Okay, I was just using those two as an example :)
"If you look at some other non real numbers which are still numbers like imaginary numbers. there value is also impossible to define it is unknown is 1i is greater than or less than 2i"
1i = 2i
"Or infinitesimal numbers, the most popular of which famously known as the smallest number which is not zero. these are a type of surreal number because you know where they fit on the number line. except they aren't there. Right after zero but before anything els. Unfortunately no such spot accually exists so its not a real number."
Funny story, similar to how there is an absolute 0 in kelvin when referring to the temperature of an atom until the moment where nothing within it moves any longer. some people suggest there is an absolute 0 within numbers in general. So if I was to say the limit of all numbers is -100 up until 100.
The chart would look like this... 0, -100, -99, -98.... -3, -2, -1, - , 1, 2, 3... 98, 99, 100
Since we are in a place where we have finite equations, there simply is no infinite value to it, we can only clarify variables to be in this range as there is no parameter to guide said variable.
For example, if I was to measure a force, and it was 1/3 of 10, the force would be a numeral that we regard as infinite, but when we measure a finite equation and the force is applied to something, in the end we have an answer, it does not normally become a number that doesn't finish.
Similar to zeno's paradox
"In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise"
Even though there is an infinite amount of numbers, the result is still finite, the runner will still win the race.
making the idea of a number being infinite a principle rather than an actual number.
1. an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations.
1. amount to (a specified figure or quantity); comprise
2. mark with a number or assign a number to, typically to indicate position in a series.
Basically, we define a number as something with a place, or something with value. With infinity, it has no place because it's just the highest thing possible, it's like a race and calling it first place. But then it's higher than that because you can't limit infinity, even the highest thing you could imagine, the term infinity makes that look like an atom.
Therefore, infinity is a principle and a philosophical term in math.
mshoosterman forfeited this round.
1 votes has been placed for this debate.
Vote Placed by Lexus 1 year ago
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