2006-10-20 11:27:47 · 15 answers · asked by ixat02 2 in Science & Mathematics ➔ Mathematics
The difference between Mathematics and Mysticism
There is no "smallest number greater than 0". This is not only because Mathematicians are self-centred egotists, or even because maths profs are Mathematicians (see above) who wish only to flunk their students.
Mathematics believes in doing well-defined things (ONLY). It's practically the science of well-defined things. Having a smallest positive number would break this. For suppose such a number e existed. Then we know e > 0, so e > e/2 > 0, which is a contradiction (e/2 is a smaller positive number!).
So no such thing exists. And you cannot meaningfully "define" something to be this nothing. There is no number 1/infinity, no number 1/aleph0, no number 1/ω, and no number 0.00...001 (where there are "infinitely many" 0's between the decimal point and the 1). None of them make sense, none of them are defined, and all of them are even more nonsensical than the idea of a smallest positive number e as above. And don't get me started on 0.99999...; it really does equal 1 (and no, 1-0.999... is not such a "smallest number greater than 0").
2006-10-20 11:39:30 · answer #1 · answered by Anonymous · 1⤊ 0⤋
0+
2006-10-20 11:29:38 · answer #2 · answered by Dr. J. 6 · 0⤊ 0⤋
basically writing a style in any notation or following any kit of numerals would not make it extra powerful or smaller It keeps to be an comparable. In scientific notation ninety 8.4 is written as 9.80 4*10^one million. Its order of fee technically is1 yet 9.8 is extremely very almost such as 10, that's extremely very almost on the brink of a style with order of fee 2. working occasion one hundred or 123 is assorted order of fee 2.
2016-12-16 11:05:21 · answer #3 · answered by ? 3 · 0⤊ 0⤋
undefined.
You could, for example, start with 1, and divide by 2, and do this for as long as you'd want, getting ever smaller numbers that would never be 0 (though the limit of 2^-n, for n tending towards infinity, is indeed 0).
2006-10-20 12:08:54 · answer #4 · answered by AntoineBachmann 5 · 0⤊ 0⤋
Suppose that there was such a number. Let's call it epsilon. Since epsilon is larger than zero it must be positive. Then we have epsilon over two is also positive but smaller than epsilon itself. This is a contradiction. Therefore no such number exists.
2006-10-20 12:43:50 · answer #5 · answered by dimenti0 1 · 0⤊ 0⤋
I think the question is what number is smaller than one and bigger than minus one.
2006-10-20 11:37:21 · answer #6 · answered by Charlotte C 3 · 0⤊ 0⤋
.5 or 1/2
2006-10-20 11:31:22 · answer #7 · answered by Anonymous · 0⤊ 1⤋
Any number, no matter how small, can be divided into a smaller number. Therefore, the number is infinity.
2006-10-20 11:33:33 · answer #8 · answered by John Doe 1 · 0⤊ 0⤋
0 + 1/infinty
2006-10-20 11:33:39 · answer #9 · answered by hackmaster_sk 3 · 1⤊ 0⤋
When anybody gives an extremely small number n, I know one much more smaller one: n/(10!^100!)!
Th
2006-10-20 11:31:34 · answer #10 · answered by Thermo 6 · 1⤊ 1⤋