Quantity: Difference between revisions
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Quantity is the most fundamental concept of math. Other concepts almost as fundamental are [[shape]] and [[likelihood]] [TODO really? think about it]. | Quantity is the most fundamental concept of math. Other concepts almost as fundamental are [[shape]] and [[likelihood]] [TODO really? think about it]. | ||
We observe that quantity comes in two forms. | We observe that quantity comes in two forms: multitudes and magnitudes. A quantity is said to be a multitude, when there is some restriction on how it could be divided into parts. A quantity is said to be a magnitude, when there is no restriction on how it could be divided into parts.<ref>[TODO I got these from Aristotle, ''Metaphysics'', Book V, Ch. 11-14 ]</ref> In Objective Mathematics, the notion of a "continuous quantity" is used interchangeably with magnitude, and the notion of "discrete quantity" is used interchangeably with multitude. | ||
Number is the concept which measures quantity. | |||
Discrete quantities are measured by [[natural numbers]]. Continuous quantities are measured by [[Fractions|fractional numbers]]. [todo what about like differences, or <math>\sqrt{2}</math>? don't both of those things also measure quantity?] | |||
Discrete quantities are measured by [[natural numbers]]. Continuous quantities are measured by [[Fractions|fractional numbers]]. | |||
== Examples == | == Examples == | ||
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The distance to the sun | The distance to the sun | ||
== References == | |||
Revision as of 00:25, 22 January 2024
[TODO under construction]
Quantity is an irreducible attribute of existents, and therefore it admits only an ostensive definition.
When one says that there is more or as much or less of A than there is of B, he is comparing the quantity of A to the quantity of B.
When one talks about adding to or subtracting from A, he is talking about a change in the quantity of A.
Quantity is the most fundamental concept of math. Other concepts almost as fundamental are shape and likelihood [TODO really? think about it].
We observe that quantity comes in two forms: multitudes and magnitudes. A quantity is said to be a multitude, when there is some restriction on how it could be divided into parts. A quantity is said to be a magnitude, when there is no restriction on how it could be divided into parts.[1] In Objective Mathematics, the notion of a "continuous quantity" is used interchangeably with magnitude, and the notion of "discrete quantity" is used interchangeably with multitude.
Number is the concept which measures quantity.
Discrete quantities are measured by natural numbers. Continuous quantities are measured by fractional numbers. [todo what about like differences, or ? don't both of those things also measure quantity?]
Examples
Discrete quantities
The number of apples in the grocery store is a discrete quantity. Although...
The number of oxygen atoms in a room
The size, in bits, of some file on some computer
The number of ingredients in a recipe
The price of a washing machine
Continuous quantities
The height of a man
The speed of a car
The volume of a swimming pool
The weight of a bag of rice
The distance to the sun
References
- ↑ [TODO I got these from Aristotle, Metaphysics, Book V, Ch. 11-14 ]