/word ~ logos (knowledge) ~ wisdom ~ .../

https://www.youtube.com/watch?v=aGFNGH9jHyM

(January 18, 2022 at 1:30 pm)polymath257 Wrote: Computer scientists and set theorists start counting at 0. Most other people start counting at 1.

But, in set theory, 0 is a natural number and is identified with the empty set, just like 1 is identified with the set containing just the empty set.

(May 20, 2023 at 4:21 am)Carl Hickey Wrote: ...

= = =

Lateral (complex) numbers: oriented line segment (vector, 1 d) in a plane (2 d).

a (length, angle), b (length, angle)

c = a . b (length (a) . length (b), angle (a) + angle (b))

-

(-2) . (-3) = 6 (2 . 3, pi/180 + pi/180 = 2 pi/360/0)

i (1, 90)

i . i = -1 (1 . 1, 90 + 90 = 180)

= = =

Natural numbers were created by God, everything else is the work of men.
Kronecker (1823–1891).

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In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. Through Him all things were made, and without Him nothing was made that has been made. In Him was life, and that life was the light of men. The Light shines in the darkness, and the darkness has not overcome it.

...
/word ~ logos ~ wisdom ~ .../

Gospel of John

Hi,

On YouTube there is a video made by a young mathematician. He uses cardboard boxes (empty boxes in boxes) to visualise the idea.
I'll place the link after my 30th post here.

(May 21, 2023 at 12:46 am)Carl Hickey Wrote:

(January 18, 2022 at 1:30 pm)polymath257 Wrote: Computer scientists and set theorists start counting at 0. Most other people start counting at 1.

But, in set theory, 0 is a natural number and is identified with the empty set, just like 1 is identified with the set containing just the empty set.

(May 20, 2023 at 4:21 am)Carl Hickey Wrote: ...

= = =

Lateral (complex) numbers: oriented line segment (vector, 1 d) in a plane (2 d).

a (length, angle), b (length, angle)

c = a . b (length (a) . length (b), angle (a) + angle (b))

-

(-2) . (-3) = 6 (2 . 3, pi/180 + pi/180 = 2 pi/360/0)

i (1, 90)

i . i = -1 (1 . 1, 90 + 90 = 180)

= = =

Natural numbers were created by God, everything else is the work of men.
Kronecker (1823–1891).

= = =

In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. Through Him all things were made, and without Him nothing was made that has been made. In Him was life, and that life was the light of men. The Light shines in the darkness, and the darkness has not overcome it.

...
/word ~ logos ~ wisdom ~ .../

Gospel of John

Hi,

On YouTube there is a video made by a young mathematician. He uses cardboard boxes (empty boxes in boxes) to visualise the idea.
I'll place the link after my 30th post here.

To clarify, it's 30 posts AND 30 days.

(January 18, 2022 at 7:34 am)GrandizerII Wrote: The answer depends on the class you're taking. Sometimes it's considered a natural number, sometimes it's not.

Couldn't locate the segment using the timestamp you posted. What's the argument exactly?

natural (adj.)

c. 1300, naturel, "of one's inborn character; hereditary, innate, by birth or as if by birth;" early 14c. "of the world of nature (especially as opposed to man)," from Old French naturel "of nature, conforming to nature; by birth," and directly from Latin naturalis "by birth, according to nature," from natura "nature" (see nature).

...

etimonline

=

nature (n.)

late 13c., "restorative powers of the body, bodily processes; powers of growth;" from Old French nature "nature, being, principle of life; character, essence," from Latin natura "course of things; natural character, constitution, quality; the universe," literally "birth," from natus "born," past participle of nasci "to be born," from PIE root *gene- "give birth, beget."

...

etimonline

= 

entropy (n.)

1868, from German Entropie "measure of the disorder of a system," coined 1865 (on analogy of Energie) by German physicist Rudolph Clausius (1822-1888), in his work on the laws of thermodynamics, from Greek entropia "a turning toward," from en "in" (see en- (2)) + trope "a turning, a transformation" (from PIE root *trep- "to turn"). The notion is supposed to be "transformation contents." Related: Entropic.

It was not until 1865 that Clausius invented the word entropy as a suitable name for what he had been calling "the transformational content of the body." The new word made it possible to state the second law in the brief but portentous form: "The entropy of the universe tends toward a maximum," but Clausius did not view entropy as the basic concept for understanding that law. He preferred to express the physical meaning of the second law in terms of the concept of disgregation, another word that he coined, a concept that never became part of the accepted structure of thermodynamics. [Martin J. Klein, "The Scientific Style of Josiah Willard Gibbs," in "A Century of Mathematics in America," 1989]


etymonline

=

...

== =

Latin and Greek and invented and ... other words are used in science. Naming is a kind of (an?) art.

In some languages Latin and Greek and other scientific terms are translated. 

Language is all about politics.

The point is that "natural" different ones take it differently.

Also,

things which one sees, hears, ... are one's thoughts. They (the things) are "inside one's head".

What is "outside outside one's head" is theoretical.

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Clausius invented the word entropy as a suitable name for what he had been calling "the transformational content of the body."

He meant that.  
/a link will be placed/

Later "entropy" received different meanings.

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War is too serious a matter to entrust to military men. / War is too important a matter to be left to the military.

Georges Clemenceau

The same is with language. It is too serious a matter to be left to the linguists.
/there is not language/

Yes, I've picked quite a few of them.

It depends how you define natural. I don't like the number 0, so I voted no out of spite.

(June 18, 2023 at 7:42 am)SirLuck Wrote: It depends how you define natural. I don't like the number 0, so I voted no out of spite.

Welcome Woof new entity!

Hi,

= = =

Full set and empty set are complementary ("logical opposites").

The State/Quality of a full set is a natural number.

The State/Quality of an empty set is Zero.

To get to "Zero" one goes through "logical opposites" (one more step).

Empty set manifests itself indirectly (so does Zero).

= = =

post #73
Carl Hickey: On YouTube there is a video made by a young mathematician...

What IS a Number? As Explained by a Mathematician
https://www.youtube.com/watch?v=dKtsjQtigag

/23:36 min. - the beginning/



Ernst Zermelo
https://en.wikipedia.org/wiki/Ernst_Zermelo

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Is 1 a Prime Number?
https://www.youtube.com/watch?v=R33RoMO6xeA