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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.<ref>I took this definition from Harry Binswanger, in his course ''Philosophy of Mathematics'', 2024. </ref>
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.<ref>I took this definition from Harry Binswanger, in his course ''Philosophy of Mathematics'', 2024. </ref>
== Is <math>\pi</math> a number? ==
[[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:
# 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. 
# 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."


== References ==
== References ==

Revision as of 23:43, 7 February 2025

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.[1]

Is a number?

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."

References

  1. I took this definition from Harry Binswanger, in his course Philosophy of Mathematics, 2024.