March 21st, 2015, 07:58 AM  #21 
Senior Member Joined: Mar 2015 From: England Posts: 201 Thanks: 5 
10 Infinitithes = 1 smallest finite number Zero is known as a number because it is shown on the number line. Zero is at the start, Infinity would be at the end. Last edited by HawkI; March 21st, 2015 at 08:01 AM. Reason: Musing 
March 21st, 2015, 08:10 AM  #22 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra 
There is no smallest number, just as there is no largest number. In fact, there is no smallest number because there is no largest number. I've already shown you that the natural definition of an infinitieth yields a value of zero. 
March 22nd, 2015, 05:59 PM  #23 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  Since "Atto" itself is defined only as a prefix, meaning "$\displaystyle 10^{18}$" so is not itself a 'thing'. But if you mean that one "infinitith" is $\displaystyle 10^{19}$, that is not at all what you were saying before!
Last edited by skipjack; March 22nd, 2015 at 07:05 PM. 
March 22nd, 2015, 07:04 PM  #24 
Global Moderator Joined: Dec 2006 Posts: 20,927 Thanks: 2205  
March 23rd, 2015, 03:34 AM  #25 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,157 Thanks: 732 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
The closest equivalent I can think of is "infinitesimal" which is used in calculus and perturbation theory as a place marker to study tiny changes in something. It has the prefix $\displaystyle \delta$ or $\displaystyle d$. For example, if $\displaystyle x$ is a Cartesian spatial coordinate, $\displaystyle \delta x$ refers to a very tiny (but finite) change in length and $\displaystyle dx$ refers to an infinitesimally small change in length. There are special rules about you deal with these in a consistent manner in calculus though; treating them as standard "numbers" will typically get you into trouble. If this is not what you mean, then you should probably reread V8Archies post about limits. 
March 23rd, 2015, 05:12 AM  #26 
Senior Member Joined: Mar 2015 From: England Posts: 201 Thanks: 5 
I think I read some where Infinity  1 = Finite I only mentioned atto because that was the smallest number I could think of, I'm going to choose the third spelling. cm = centre metre im = infinitith metre 1cm = 1cm 1im = 1im 10im = finite Last edited by HawkI; March 23rd, 2015 at 05:13 AM. Reason: Addendum 
March 23rd, 2015, 05:45 AM  #27 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra 
You are talking rubbish. The thing you have named does not exist  or if it does, it is already called zero.

March 23rd, 2015, 06:10 AM  #28  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,157 Thanks: 732 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
Here's a list of prefixes for very small numbers used in maths and sciences, using metres as an example unit: 1 metre = 1m = 1m 1 millimetre = 1 mm = $\displaystyle 10^{3}$ m 1 micrometre = 1 $\displaystyle \mu$ m = $\displaystyle 10^{6}$ m 1 nanometre = 1 nm = $\displaystyle 10^{9}$ m 1 picometre = 1 pm = $\displaystyle 10^{12}$ m 1 femtometre = 1 fm = $\displaystyle 10^{15}$ m 1 attometre = 1 am = $\displaystyle 10^{18}$ m 1 zeptometre = 1 zm = $\displaystyle 10^{21}$ m 1 yoctometre = 1 ym = $\displaystyle 10^{24}$ m Another very small length is 1 plank length = $\displaystyle \ell_P$ = $\displaystyle 1.6162 \times 10^{35}$ m ... no "infinitieth" here. All of these numbers are finite, no matter how small. Even $\displaystyle 10^{100000000}$ would be finite. Even 1 divided by Graham's number would be finite!  
March 23rd, 2015, 06:18 AM  #29 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
You're thinking that there is some threshold number $0<\varepsilon\in\mathbb{R}$ such that anything $0<x<\varepsilon$ is 'infinitesimal' and anything $x>1/\varepsilon$ is 'infinite'. Sure, you could do that, but I don't see any advantage to doing so  and clearly this contradicts mathematical usage of those terms.

March 23rd, 2015, 09:17 AM  #30 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra  This is just plain wrong. What ever finite quantity you subtract from an infinite one, you are left with an infinite quantity. This glosses over whether the term 'an infinite quantity' means anything. Probably we should talk about taking a finite number of elements from an infinite set. Although some people would deny the existence of infinite sets too. 

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