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Scientists also use "infinity" quite a bit. Of course, infinity can never be stored in a computer or written down, since there aren't enough particles in the universe to do so, but it is a perfectly legitimate tool, and it's something most physicists are comfortable slinging around.

Quote from: jpetruccelli on 21/09/2007 06:58:01Scientists also use "infinity" quite a bit. Of course, infinity can never be stored in a computer or written down, since there aren't enough particles in the universe to do so, but it is a perfectly legitimate tool, and it's something most physicists are comfortable slinging around.Infinity is not a number, it is a concept - it can have no numerical value.

Yes and no. It's not a number in the traditional sense of a real or complex number. However, it is a number in the sense that it can be used to count and measure things.

Generally as used in physics, it is not a number, but a concept of making something arbitrarily large.

In the sense of this question, though, infinity (or technically limit:x->infinity) pretty much describes the whole concept of the scientist sitting in a room constantly counting higher and higher...

Despite the vast inventory of numbers opened up by these studies, it is remarkable that the arguably 8 most important numbers in mathematics lie within a small zone near the number 2. They are:01sqrt(2) = 1.41421....sqrt(3) = 1.732.....2 (basis of computers)e = 2.7182818....pi = 3.1415926.....i , absolute value = 1

I feel that 10 should rank as the most important number as all arithmetic is based on it.Some arithmetic to the base of 2, 8 or 16 is used in the computer world but in the real word 10 is always used

Quote from: jpetruccelli on 22/09/2007 06:28:57Yes and no. It's not a number in the traditional sense of a real or complex number. However, it is a number in the sense that it can be used to count and measure things.If you can count it, it is not infinite. If you can measure it, it is not infinite. In certain cases, you can say you can do algebra with it, but it is neither physically countable nor physically measurable.

Quote from: jpetruccelli on 22/09/2007 06:28:57Generally as used in physics, it is not a number, but a concept of making something arbitrarily large.If that is how you are using the term infinity, then it is the wrong usage. Infinity is not a number that is arbitrarily large, it is a number that is provably uncountably large (i.e. if you believe it is a countable number, merely too large to be counted for practical reasons, then it is not infinity).

Quote from: jpetruccelli on 22/09/2007 06:28:57In the sense of this question, though, infinity (or technically limit:x->infinity) pretty much describes the whole concept of the scientist sitting in a room constantly counting higher and higher...You can prove that pi is an infinitely long number when expressed as a decimal value, but that is because you can show theoretically that you cannot ever possibly (not merely impractical to, but it is physically impossible to) count the total number of digits of pi in decimal notation.

Even 2, 8, and 16, are still used in a number of imperial weights and measures; but even though imperial units are beginning to fall out of favour, there is no evidence that anybody in the foreseable future will use units of time that are not based on multiples of 12 (24 and 60 are both multiples of 12).

It is though interesting that you regard i (imaginary 1) as more important than -1 (negative 1),

To regard sqrt(2) and sqrt(3) as important seems somewhat arbitrary to me (sqrt(2) comes up quite often, but sqrt(3) is somewhat rarer).

You can also define two types of infinities used in counting "countably infinite" (what you get if you count the real numbers) or "uncountably infinite" (what you get if you count the rational numbers).

QuoteYou can also define two types of infinities used in counting "countably infinite" (what you get if you count the real numbers) or "uncountably infinite" (what you get if you count the rational numbers). No, this is inaccurate. The type of infinity associated with integers and that which is associated with rational numbers is the same. The proof is elementary: To the field of rational numbers, line up all the numerators along the x axis and all the denominators along the y axis. Now create a path starting from (0,0) and zigzagged back and forth diagonally, taking in row after row of diagonal dots. The order in which those dots occurs on the zigzag path constitutes an assignment of each to an integer, in order. However, because each represents a rational number, you end up with a one to one correspondence between rational numbers and integers. In fact, it is even more remarkable because many of those dots actually represent the same rational number, but not reduced to lowest terms. So that according to that, one would expect the number of integers to exceed that of rational numbers, but that cannot be of course because integers themselves are rational numbers. This is bizarre and counterintuitive, but demonstrates that integers and rational numbers are of the same order of infinity. Now there is indeed a higher order of infinity, and I believe it belongs to the set of all real numbers. I further understand that it is possible to create sets having even higher distinct orders of infinity, I think they are called the Alephs, which can be arranged in order from Aleph 0 on up to Aleph as large an integer as we want, Aleph 0 corresponding to the level of enumerable sets such as integers and rational numbers.