/sci/ - Science & Math

[Anonymous No.12661874]

> A number is a mathematical object used to count, measure, and label.
>Counting is the process of determining the number of elements of a finite set of objects.
>Measurement is the numerical quantification of the attributes of an object or event, which can be used to compare with other objects or events.
>Nominal numbers are categorical, which means that these are numerals used as labels to identify items uniquely.
All three of the main ways that Wikipedia describes numbers invoke the word number in their own definition. Is this like how linguists have difficulty escaping the self-referentiality of pure language, where a real language must rooted in something intuitive or experienced?

Also, without making Wikipedia’s error: What is a number?

[Autolycus No.12661959]

I dunno' what most maths people might say, but I like Whitehead, so
>When Whitehead and Russell logicized the concept of number, their starting point was our intuition of equinumerous classes of individuals—for example, our recognition that the class of dwarfs in the fairy tale of Snow White (Doc, Grumpy, Happy, Sleepy, Bashful, Sneezy, Dopey) and the class of days in a week (from Monday to Sunday) have ‘something’ in common, namely, the something we call ‘seven.’ Then they logically defined (i) classes C and C to be equinumerous when there is a one-to-one relation that correlates each of the members of C with one member of C, and (ii) the number of a class C as the class of all the classes that are equinumerous with C.

>When Whitehead logicized the space of physics, his starting point was our intuition of spatial volumes and of how one volume may contain (or extend over) another, giving rise to the (mereo)logical relation of containment (or extension) in the class of volumes, and to the concept of converging series of volumes—think, for example, of a series of Russian dolls, one contained in the other, but idealized to ever smaller dolls. Whitehead made all this rigorous and then, crudely put, defined the points from which to further construct the geometry of space.

[Anonymous No.12661984]

>>12661874
>A number is a mathematical object used to count, measure, and label.
this one is fine
>Counting is the process of determining the number of elements of a finite set of objects.
Counting is the process of determining 'how many' elements there are in any finite set, physical or imaginary (can probably lose that part but I prefer the clarity)
>Measurement is the numerical quantification of the attributes of an object or event, which can be used to compare with other objects or events.
Measurement is the collection of data and values attributed to any quantifiable set, usually in a numerical form.
>Nominal numbers are categorical, which means that these are numerals used as labels to identify items uniquely.
Nominal numbers are different from countable quantifiable values as they are instead used as a form of categorization language. Nominal numbers do not, and often don't follow the rules of measurement but rather their own arbitrary system.

[Anonymous No.12662039]

>>12661959
Unironically bretty good

[Anonymous No.12662170]

>>12661874
All mathematics requires axioms, which are defined notions that are taken as true without proof or evidence, as well as undefined notions, which are not axioms, they are pieces of human knowledge and intuition that are used to define the axioms.

[Anonymous No.12662188]

>>12661874
Defining an entity separate from the Universe according to predetermined parameters.

[Anonymous No.12662664]

>>12661959
good explanation.
theres no way out of the issue of conciouness. one of the very basics blocks of conciousness is "differentiation" out of that comes "pattern recognition" math is intrinsically pattern recognition (logical structuring) there's a theological analogy where god is the first entity to differentiate: "light from darkness" "the waters below from the heavens above", "in the beginning was the word/Logos"(meaning a structure, words/language are logical patterns/structures)...adam is commanded to: "name the different animals"

as it is conciousness is metaphysical (until it is proven that it is "just a computation") this means language and math are both metaphysical in nature, this is in principle why math can not be proven outside the limits of our own logical structure (our conciousness, our pattern recognition capability) the ultimate truth of math directly depends on the truth of human conciouness

[Anonymous No.12663206]

>>12661874
number is a label for emotional processes that expend similar amounts of energy

there is a process in the brain that produces the same product when seeing seven of one thing and seven of another or counting seven breaths to measure time, those products and the biases they create in the mind together are numbers

[Anonymous No.12663225]

>>12662170
braindead lies
you can describe anything you can perceive and then perceive more closely by this description

you might be delayed by your lack of mind development, you might be delayed by your lack of genetic development, you might be delayed by a lack of development of instruments to induct data, but you can always deduce facts of history

[Anonymous No.12663341]

You can define numbers through the properties of bijections and surjections between sets

[Anonymous No.12663367]

>>12661874
Numbers can be expressed without words as in a tally. Ratios may be more primitive still. Alot, less, more, some, most, greater, etc. A handful of BOOBA describes a lesser bound of size, unique to a hand. I don't think counting, or the difference between numbers, is the quintessential essence of number at all.

[Anonymous No.12663373]

>>12661874
Natural numbers can be recursively defined:
A natural number is either zero, or the successor of a natural number. There are no natural numbers whose successor is zero.
I guess you could ask what successor really means here, you can use set theory to make that notion rigorous, but really you just move the problem because then we have to ask what a set really is.

[Anonymous No.12663395]

>>12661874
[math]\emptyset[/math]
[math]\{\emptyset\}[/math]
[math]\{\emptyset, \{\emptyset\}\}[/math]
and so on, and so on

[Anonymous No.12663422]

>>12663395
sets seem a lot harder to define than numbers

[Anonymous No.12663445]

>>12663225
There are no lies in this post >>12662170

[Anonymous No.12663481]

>>12663422
That's the point. You can define numbers as sets, but you can't define sets as numbers. Study some axiomatic set theory, it's pretty fun.

[Anonymous No.12663509]

>>12663395
If you go that route, you should not only mention those objects that are numbers, but also all those that are not numbers.

[Anonymous No.12663553]

>>12663481
Sets are like lego bricks. Once you know the defining properties of numbers, you can make sets to piece together models of all the numbers. So you begin from the idea that there is one particular fixed thing called all the numbers. But you discover that when you have sets, you can build uncountably many non-isomorphic countable sets each of which has precisely the properties required of the collection of all the numbers. Which does not even take into account all the different models of the natural numbers that are uncountable.

[Anonymous No.12664329]

>>12663225
You're the braindead here
>you can describe anything [..]
That's the thing right here. To describe (or define) something, you need a language. That applies to the definition of the language you're using, i.e. a language can only be expressed in terms of another language.
That's what we're doing with axioms. They're the base language for mathematics, and because we have no choice but informal and intuitive english to describe axioms, we've made them sufficiently simple so that's not a problem.

[Anonymous No.12664344]

>>12663481
>you can't define sets as numbers. S
Yeah, but thats because you cant define sets as anything at all, theyre completely meaningless objects (as Godel and Cohen showed).

[Anonymous No.12664356]

>>12663341
Sets are undefined and meaningless so that's not a good definition.

[Anonymous No.12664370]

>>12664329
idk to me it really just sounds like philosophy is crossing over into math and its not really important/has anything to do with counting
>>12662170
no the only thing understanding math takes is being alive with a functioning brain. Humans and animals both are really good at counting, in fact its innate. Regardless you dont need language or axioms for numbers and counting. pic related

[Anonymous No.12664971]

>>12661874
A correspondence between real objetcs like a rock and words in the mind like "one".
when you make this correspondence the rest is derive from this.

[Anonymous No.12665243]

>>12661874
>numbers describes the proportionality of objects relative to other objects
simple as

[Anonymous No.12665817]

>>12661874
A number is a communication signal for division of labour or a distribution of resource. The rest of my post is me wanking.

Now this is interesting. As a linguist yes it is very difficult to escape the self-referential nature of explaining that which is ultimately grammatical orientation of a vectorized class of identities who hold varying degrees of language skills (vocabulary vs. predicates). One either ends up losing people in the swamp of variables (*semantic synonyms) or trapping people into some semantic echo chamber of simplicity.

A real language ultimately though does conform to the three basic signal satisfaction rule: Hungry, Happy, Horny.

Essentially resource acquisition (or stockpiling), experience variation (or complexification), and reproductive expression (or expressive recognition).

Ultimately though a number is just a reported grouped abstraction value of a given observation of objects. It is something that happens post-recognition.

If I have 1 apple or 1 variable makes no difference to language because bringing the focus of there being '1' thing to an audience is usually the largest portion of mental effort exerted by a human who needs to communicate the fact that there is a value at all. In English we do this by saying 'apple' or 'apples' before including numerical references because it opens up the language to 'further information may be needed to adequately inspect either a singular set or a multiplicative set'.

[Anonymous No.12665825]

>>12661984
>have 1 bucket
>fill bucket with apples
>give bucket to someone else
>do this enough times and go home and to my 7 wives who give me all the drugs, sexual servitude, and intellectual companionship that any man could ever want.

THANKS, BUCKET! I LOVE YOU! NO IDEA WHAT THESE WHITE CUNTS WANT WITH THESE BIG FUCKING UGLY RED OBLATE SPHEROIDS BUT HEY! WHATEVER FUCKING KEEPS THE CUNTS AT HOME HAPPY!

[Anonymous No.12665829]

>>12663422
How the fuck is a set hard to fucking define?

N-{Set, N}+Description = Number Theory

Number = Counting ÷ Null
Theory = Wank-talk

[Anonymous No.12665844]

>>12664344
>N mathematicians try to define N
>N-results occur

Gee, I wonder if mathematicians have some other agenda for not agreeing on what a number fucking is when it comes to winning "who has the bigger number" argument.

>t.cave mathematician