Number

A number is an identification of a quantity, by means of a symbol whose position in a fixed sequence of those symbols is the same amount as that which is being identified.

Is a fraction a number?

Yes.

To identify a quantity as Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p/q} is to say that it consists of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p} pieces of quantity Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1/q} . It is not fundamentally different from identifying a quantity as Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p} ; it's just that the unit is different. In the fraction, the unit is being regarded as a Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle q} th of another unit.

Is a negative a number?

Yes.

We can consider a sequence that goes backwards; 1, 0, -1, -2, -3, and so forth. Then we can identify a quantity like -5 by putting it in correspondence with a position in that sequence.

Is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \pi} a number?

No.

π is the ratio between the circumference and the diameter of a circle. Unlike standard mathematics, by "circle," OM means real, finite, physical circles, with thickness and height and bumps and other non-uniformities. Observe the following facts about OM's concept of π, which are not true of the standard concept:

1. Since π is the result of a continuous measurement, it is not a specific value, but is rather a range of possible values. For example, one circle might have a circumference and diameter whose ratio is found to be 3.1 ± 0.1.
2. π is not the same range for every circle. For one circle, we might measure π = 3.1 ± 0.1; for another we might measure π = 3.15 ± 0.02; for yet another, we might measure π = 3.14159 ± 0.00005.

OK I'm failing to differentiate between two things. On the one hand, there's the actual ratio of the actual circumference and diameter of the actual circle. On the other hand, there's the thing we measure....

To treat something as a circle is to say like "all these ways in which I might measure its circumference, they're the same."

Is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{2}} a number?

No, I don't think so.

First of all we must settle on a definition of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{2}} . There are two potential definitions that I can think of

1. (The usual definition) Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{2}} is the number that squares to 2.
2. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{2}} is the side length of a square of area 2.

If definition 2 is correct, then Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{2}} is not a number, for basically the same reason that π is not a number. It seems that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{2}} defines a range of numbers (and one which, to boot, differs between concrete situations) rather than a specific number.

If definition 1 is correct, then what is the fixed sequence of symbols which we are using to identify Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{2}} ? It's certainly not fractions. I don't think can be anything else, either.

Is a number just "an identification of a quantity"?

No.

My sofa has some length. In saying that, I have identified a quantity, but I haven't given a number.

Is an element of the cyclic group Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{Z}_n} a number?

Yes, I think so.

For example, an amount of time could be identified by saying something like: after that much time has passed, it will be 4:00.

We are identifying the amount of time by drawing a comparison between it and a "sequence" of fixed symbols appearing on a clock. This sequence is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{Z}_{12}} , or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{Z}_{12} \times \mathbb{Z}_{60}} , or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbb{Z}_{12} \times \mathbb{Z}_{60} \times \mathbb{Z}_{60}} , depending on the clock.