Jolt Country

It has been suggested that we have a thread to discyss mathrmatical topics. If this becomes interesting, we might split off separate discussions on parpticular mathematicsl topics ti their own separate thread.

Okay, let's consider the following:

• Mathematics is the only science where a Theory can be "proven." In all other subjects, like the Theory of Gravity, or the Theory of Evolutuon, all that can ever be said about a well-studied and researched Theory is that the evidence so far tends to support its conclusions. This keeps the proponents of a Theory honest, in that research has to be open and published, on a peer-reviewed basis, where the hypitheses proposed can be checked and verified, and if erroneous, falsified. So, remember, the next time some magazine claims science had "proven" some Theory that is non-mathematical, you can know that they have no idea what they are talking about.
• The term "infinity" - represented by the turned on its side 8 symbol ∞ - has no specific value, and can have multiple meanigs. I'll offer an example: the number of possible integers - whole numbers without a fractuon - is infinite, or infinity. But, how many fractional values - like .5 or 3/16 are there between any two successive integers, e.g. between 0 and 1, or between 98 and 99? That's right, it's also infinity.
  
  So think about this: The number of positive integers, or the number of fractions between any twi consecutive numbers, ae borh the same, infinity. But, combine the two all of the whole and fractional positive numbers is not "double infinity" - there is no such thing - it is alsi referred to.as just "infinity".
• Thw number Pi - Π - has, as far as we can tell, an infinite number of non- repeating digits to the right of the decimal point. Most people who've ever neefed to do a serious calxulation has memorized pi to a few digits - i remember it as 3.14159268 - but some peopke have memorized it to thousands of digits, and I think thr currebt record is one million, but through use of computers, we have calculated pi to one billion digits. Apparently the number has no repeating sequences.
• As a tie-in to the prior item, a typical calculation using pi only needs a few digits because the eztra precision isn't necessary (tbe classic definiton of 'diminishing returns") and huge precision levels of pi are just intellectual exercises. What do you think is a reasonable number of digits to use of PI?
• An episode of Star Trek: The Next Generation has a mention of Fermat's Last Theorem from 1665, which reads

  Following his death, a mathematical equation was found scrawled in the margin of his notes, "xn + yn = zn, where n is greater than 2," which Fermat said had no solution in whole numbers, but he also added a phrase, "remarkable proof."

  Fermat didn't shiw the proof. In the story, oeople were still trying to fins the proof, 209 years from now. But, just three years after the show was filmed, someone would solve thr proof. So, if you know of any mathematical ideas, that haven't' been solved or proved, that you think we will find it. Perhaps giving a time frame, e.g. within 5,10 or so.many years.

So here' s your turn: discuss one (or more) of these, or pick one of your own and tell us abput it..

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Sent from a mobile phone.

Tdarcos wrote: Fri Jan 27, 2023 1:00 am Mathematics is the only science

Mathematics is not actually a science. So you started on the wrong foot there.

BAD START.

On Fermats last theorem, my abstract algebra professor, Naomi Jachonowitz, is somewhere in the fine print of people that helped work on the solution.

The most beautiful equation in Mathematics is called Eulers identity because if you take an imaginary number to the exponential, you get the equation of a circle .

e^(i(pi))+1=0 if I remember correctly.

e^(i(pi))

Ignore the second e^(i(pi)) there in the above explanation. I don't know how that got there.

(Drags hairy knuckles on floor)

I like vanilla....

2+2=5

Come on Tdarcos! Get your shit together.

I liked tdarcos's explanation of "different sizes of infinity." A math professor would have written a big list of decimal numbers stacked on top of each other and said "now now take the diagonal of this infinite square of numbers and that's a new number that is also of size of infinity."

It's also almost backhandedly programmed into the categorization of numbers. Is it a real number?imaginary? Rational? Aren't their more real numbers [R] than their are natural numbers [N]?

RealNC wrote: Fri Jan 27, 2023 5:14 am

Tdarcos wrote: Fri Jan 27, 2023 1:00 am Mathematics is the only science

Mathematics is not actually a science. So you started on the wrong foot there.

Okay, maybe I am wrong. Let's see the definition of "science":
Ahh, first one that comes up:

1. (countable) A particular discipline or branch of learning, especially one dealing with measurable or systematic principles rather than intuition or natural ability.

Now, I was going to ask you to explain how, "mathematics is not a science," but, the same source has the following:

Usage notes
Since the middle of the 20th century, the term science is normally used to indicate the natural sciences (e.g., chemistry), the social sciences (e.g., sociology), and the formal sciences (e.g., mathematics). In the 18th and 19th centuries, the term was broader and encompassed scholarly study of the humanities (e.g., grammar) and the arts (e.g., music).

Okay, now explain why mathematics is not a science.

raecoffey wrote: Fri Jan 27, 2023 7:29 am Ignore the second e^(i(pi)) there in the above explanation. I don't know how that got there.

You were hungry and wanted a second slice of pi?

The REAL Real Man wrote: Fri Jan 27, 2023 10:24 am 2+2=5

But only for large values of 2.

Ice Cream Jonsey wrote: Fri Jan 27, 2023 11:33 am Come on Tdarcos! Get your shit together.

I did. The general consensus is that Nikos is wrong. I have found others that agree with my usage, including dictionary.com, ("a branch of knowledge or study dealing with a body of facts or truths systematically arranged and showing the operation of general laws") and Merriam-Webster , ("knowledge or a system of knowledge covering general truths or the operation of general laws especially as obtained and tested through scientific method").

I'd say this is one of a very small cases where I was not only right, I was conclusively right.

raecoffey wrote: Fri Jan 27, 2023 12:22 pm It's also almost backhandedly programmed into the categorization of numbers. Is it a real number?imaginary? Rational? Aren't their more real numbers [R] than their are natural numbers [N]?

The problem is that "infinity" or an "infinite" number, is, by definition, uncountable. So, to answer that, we have to use set theory instead, and I think a Venn diagram works here.

While most Venn diagrams are horizontal, I decided to be vertical. While all of these (including the box) in and of themselves are infinite, the three inside the box are a subset of infinite.

I just thought of a great idea for a name: "uncountable numbers" and a definition "a quantity or a set of numbers with a magnitude exceeding the number of atoms in the universe."

So, while the box contains an infinite number of items, each of the segments of the Venn diagram (and the box) contain an uncountable number of values.

Man, you better know your infinity, mister, because you sure don't.

Tdarcos wrote: Fri Jan 27, 2023 1:24 pm

raecoffey wrote: Fri Jan 27, 2023 7:29 am Ignore the second e^(i(pi)) there in the above explanation. I don't know how that got there.

You were hungry and wanted a second slice of pi?

Not only did I want a second slice of a nice round pi... I wanted to pair it with some from my imagination (that darned value that we call (sqrt(-2))), and I wanted to do it EXPONENTIALLY!

correct me if I'm wrong but if we expand its,
e^(i(pi))=cos(i(pi))+i(sin(i(pi))) I think?

raecoffey wrote: Fri Jan 27, 2023 2:34 pm

Tdarcos wrote: Fri Jan 27, 2023 1:24 pm

raecoffey wrote: Fri Jan 27, 2023 7:29 am Ignore the second e^(i(pi)) there in the above explanation. I don't know how that got there.

You were hungry and wanted a second slice of pi?

Not only did I want a second slice of a nice round pi... I wanted to pair it with some from my imagination (that darned value that we call (sqrt(-2))), and I wanted to do it EXPONENTIALLY!

I think there was a bumper sticker like that:
Mathematicians do it on desks, exponentially.

raecoffey wrote: Fri Jan 27, 2023 2:34 pm correct me if I'm wrong but if we expand its,
e^(i(pi))=cos(i(pi))+i(sin(i(pi))) I think?

"Wheet!"
That was the sound of your equation shooting over my head.

Ma'am, my inexcusable level of ignorance means my mathematical skills stop at fractions and general algebra. For most work as a programmer, you can 'get away' with just that. I discovered the depths of my mathematical ignorance when, at 16, with a freshly issued high school diploma given by examination, I signed up for classes at City College, one of which was one I was recommended to take - at that time, obviously, I had no idea what would be my major - a higher mathematics course, probably calculus, and the first-day test told me I had no business being in that class. I had neither the background or the training to be able to even comprehend the class, let alone solve problems in it.

I have, however, always had the humility to say, "I don't know," rather than give an answer that I might not even begin to have an idea of what a reasonable response would be.

I had an 8th grade education when i had Noel, I dropped out in 9th grade. I went back to school when she went to kindergarten at the age of 27. When I tested at MCC I was in math 098 I worked my way up, through college algebra. I figured I'd take pre-calc and trig when I got to UofR. Ther lowest math course, camc 1. I had to teach myself trig while learning calculus!

Tdarcos wrote: Fri Jan 27, 2023 2:25 pm

raecoffey wrote: Fri Jan 27, 2023 12:22 pm It's also almost backhandedly programmed into the categorization of numbers. Is it a real number?imaginary? Rational? Aren't their more real numbers [R] than their are natural numbers [N]?

The problem is that "infinity" or an "infinite" number, is, by definition, uncountable. So, to answer that, we have to use set theory instead, and I think a Venn diagram works here.

While most Venn diagrams are horizontal, I decided to be vertical. While all of these (including the box) in and of themselves are infinite, the three inside the box are a subset of infinite.

I just thought of a great idea for a name: "uncountable numbers" and a definition "a quantity or a set of numbers with a magnitude exceeding the number of atoms in the universe."

So, while the box contains an infinite number of items, each of the segments of the Venn diagram (and the box) contain an uncountable number of values.

That's all true but did you know that theirbare sizez of infinity that are the same? One class is alef(sub(knot)) that has more than one set of numbers in it. Also, did you know that you can have fixed point infinities? For example: a primitive tribe who can only count to 10. Their months last an infinite amount of days, but they end.