Lfox at 20:43, 2 July 2024

2024-07-02T20:43:40Z

← Older revision		Revision as of 20:43, 2 July 2024
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	A '''magnitude''' is a quantity with no restriction on how it can be divided into parts.<ref>Aristotle, ''Metaphysics'', Book V, Ch. 11-14</ref>		A '''magnitude''' is a [[quantity]] with no restriction on how it can be divided into parts.<ref>Aristotle, ''Metaphysics'', Book V, Ch. 11-14</ref> [TODO I'm not a huge fan of this definition.]

			== Ratio ==
			A '''ratio''' is an identification of two [[Multitude\|multitudes]].

			[TODO I mean that you identify them together, you equate one with the other. I do not mean that you say "ah this multitude is 5, and that multitude is 6." I'm not sure how to make this clear from the language.]

			To '''take the ratio''' between two multitudes is to identify them together.

			[TODO why can't I say it's the identification of a quantitative relationship between two multitudes? lol. Too vague?]

			Just like in the case of natural numbers, it turns out that many of these identifications will be the same. [TODO ?]

			I'll represent a multitude with the following notation. Suppose I identify <math>x</math> As with <math>y</math> Bs, where <math>x,y : \mathbb{N}</math>. Then I denote the ratio by <math>[x : y]_{A,B}</math>.

			=== Examples ===
			6 slices is the same as 1 pizza.

			100 pennies is the same as 1 dollar.

			1000 mm is the same as 1 meter.

			36 inches is the same as 3 feet.

			=== Facts about ratios ===
			Suppose I identify 3 As with 5 Bs. Then if I have a multitude of As given by any multiple of 3, that's the same as having a multitude of Bs given by the same multiple of 5.

			The general principle here is that <math display="block">[x : y]_{A,B} = [n x : n y]_{A,B}, \text{ for any } n : \mathbb{N}.</math>

			Now, suppose that I identify 3 As with 5 Bs, and I ''also'' identify 5 Bs with 2 Cs. Then clearly, I may also identify 3 As with 2 Cs.

			The general principle here is that <math display="block">\text{if } [x : y]_{A,B} \text{ and } [y : z]_{B,C} \text{ then } [x: z]_{A,C}</math> [TODO this doesn't make sense....]

	== References ==		== References ==

Lfox at 16:26, 2 July 2024

2024-07-02T16:26:22Z

← Older revision		Revision as of 16:26, 2 July 2024
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	A '''magnitude''' is a quantity with no restriction on how it can be divided into parts.<ref>Aristotle, ''Metaphysics'', Book V, Ch. 11-14</ref>		A '''magnitude''' is a quantity with no restriction on how it can be divided into parts.<ref>Aristotle, ''Metaphysics'', Book V, Ch. 11-14</ref>

			== References ==

Lfox: Created page with "A '''magnitude''' is a quantity with no restriction on how it can be divided into parts.Aristotle, ''Metaphysics'', Book V, Ch. 11-14"

2024-07-02T16:26:08Z

Created page with "A '''magnitude''' is a quantity with no restriction on how it can be divided into parts.<ref>Aristotle, ''Metaphysics'', Book V, Ch. 11-14</ref>"

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A '''magnitude''' is a quantity with no restriction on how it can be divided into parts.<ref>Aristotle, ''Metaphysics'', Book V, Ch. 11-14</ref>

Magnitude - Revision history

Lfox at 20:43, 2 July 2024

Lfox at 16:26, 2 July 2024

Lfox: Created page with "A '''magnitude''' is a quantity with no restriction on how it can be divided into parts.Aristotle, ''Metaphysics'', Book V, Ch. 11-14"