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March 21st, 2015, 07:58 AM   #21
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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
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March 21st, 2015, 08:10 AM   #22
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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.
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March 22nd, 2015, 05:59 PM   #23
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Quote:
Originally Posted by HawkI View Post
These words are as far as I'm aware my own invention. Perhaps this will help.

10 Infinitiths = 1 Atto
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.
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March 22nd, 2015, 07:04 PM   #24
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Quote:
Originally Posted by HawkI View Post
Let's forget about the e on the end.
Why? Did you originally intend "infinitieth or "infinitithe" or "infinitith"? Can you adopt one of those spellings and use it throughout as though the other spellings were never used (or just typos)?
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March 23rd, 2015, 03:34 AM   #25
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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.
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March 23rd, 2015, 05:12 AM   #26
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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
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March 23rd, 2015, 05:45 AM   #27
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You are talking rubbish. The thing you have named does not exist - or if it does, it is already called zero.
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March 23rd, 2015, 06:10 AM   #28
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Quote:
Originally Posted by HawkI View Post
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
If you got this from a book, I suggest you replace it with a better one!

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!
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March 23rd, 2015, 06:18 AM   #29
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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.
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March 23rd, 2015, 09:17 AM   #30
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Quote:
Originally Posted by HawkI View Post
Infinity - 1 = Finite
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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