#irrational numbers

[sidetrek]

kirk and spock are talking in the lastest update of Irrational Numbers ;)

[paintthedeadflag]

Okay, you can multiply surds together to have the effect (I say effect it is squaring them) of squaring them. So, root of 2 is irrational? So root 2 multiplied by root 2 is a natural number (which is 2 but that's not the point I'm making, or is it?).

So my question is:

Can you multiply two distinct irrational numbers and produce a rational number?

[superrealmathtricks]

Super real math trick!

It's easy to tell the difference between rational and irrational numbers!

Rational numbers know that you both just need to take a break and come back with a level head before solving the problem.

Irrational numbers will continue to yell and argue well past the point of making any sense.

[tremendously-crazy]

What are your top 5 favorite numbers, I'll go first

#1 fav: 3

#2 fav: 17

#3 fav: 221

#4 fav: ~3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034525342117 (pi)

#5 fav: 423

[thinkbolt]

The Weird Number (Xerox, 1971) - dir. William van Horn

[falseandrealultravival]

Are there more irrational numbers than rational numbers? ~ Set Theory: Mathematics Note -11 (Essay)

Cantor (1845-1918) conceived of "set theory" and used this concept to cut into "infinity". This is a field that other mathematicians have not dabbled in because of its monstrous appearance.

The weapon is "one-on-one correspondence". For example, natural numbers 1, 2, 3, 4... and even numbers 2, 4, 6...

Which one is more? Suppose you asked me. It is normal to think that "the even numbers are the natural numbers minus the odd numbers, so there are more natural numbers", but Cantor's answer is different. An even number 2 is the first, an even number 4 is the second, and so on. Since all natural numbers and even numbers can be in one-to-one correspondence, it means that there are the same number of natural numbers and even numbers. In this way, we can conclude that there are as many fractions (= rational numbers) as there are natural numbers.

"Then what about irrational numbers?" --Here is a very interesting proof. The goal is to reach a conclusion based on the law of contradiction that "there are more irrational numbers than natural numbers."

If it is possible to have a one-to-one correspondence with the natural numbers, the irrational numbers will be expressed as decimals (rational numbers will be converted to recurring decimals) and all of them will be arranged to create a list. Now, take a number that differs from the first number in the list in the first decimal place, and from the number in the second list in the second digit, and so on. The number obtained by the procedure is not in the list ! ・・・ I was able to derive a contradiction due to contradiction. Irrational numbers are infinitely more than natural numbers. In an elegant proof, this is called the diagonal argument.

Kronecker (1823-1891) raises an objection. This person was quite eccentric and professed that the natural numbers were created by God, and that all other numbers were created by humans. Kronecker seems to have had the ambition to rebuild all mathematics on the basis of natural numbers. That's why he couldn't help but hate Cantor, the guy who came to the conclusion that there are more irrational numbers than natural numbers. Kronecker persecutes Cantor at every opportunity. As a result, he suffered from mental illness and spent the last half of his life in and out of mental hospitals.

(2023.04.22)

[sidetrek]

kirk's in a little trouble but i'm sure spock will help him out this month

gonna be another update to irrational numbers by the end of sept!

[hkayakh]

So, the proof for how e (2.718…) is irrational is a long proof by contradiction that ends with ‘if e is rational, then there must be an integer between 0 and 1’. Makes sense. However, when they made that proof, they forgot to account for theta prime.

[lifeamateur617-blog]

The image of knowledge and truth as a light in the darkness of ignorance: I honestly cannot think of any other.

I think that I am not alone in obsession over the idea of fundamental truth - that in some of us it is instinctual, not chosen.

But it seems that it’s mostly procrastination; would we even know it if we found it? The idea of the search is a useful (in a material sense) distraction, just a pass time. The idea that we could put the universe into a box. The longer I look for understanding the more I think I’m bad at it.

A video I watched (from UpAndAtom on YouTube) talked about numbers, and the abundance of each of the sets of numbers. It concludes that the set of irrational numbers , which are essentially inexpressible except for a few special cases (pi, Euler’s number et al), are likely the most abundant. The idea of mathematics being largely inexpressible.

I’m a bad philosopher, but what I know says that if the universe is logical, then there must be a first cause or an infinite regress occurs.

What if universal truth is inexpressible? Is what cannot be expressed the solution of infinite regress? Are the only fundamental truths inexpressible?

I will admit, I have vested interests. I want to be someone else but I don’t want to change. I want to be true, but I can’t explain why. Is the fact that my reasoning never reaches the horizon of an inexpressible feeling proof that it’s real or am I just procrastinating?

[jim-webster]

Mastering the numbers

I freely confess that I am a poet. Confess? I have been accused of bragging about it. But still I have certain gifts and abilities. But because there is only so much one can fit into any container, I am perhaps less capable than some in one or two areas of endeavour.I suppose there is a degree of fairness in this. How would everybody else feel if I was not merely the leading poet of my…

[magickalsapphic]

to the neurodivergents and even the neurotypicals out there:

tag if you're mentally ill

[catbreadd]

Irrationals group hug!

(i is there too they are just invis c:)

[toppermostpoppermost]

JENNIFER'S BODY (2009) dir. Karyn Kusama

+bonus:

[ocudeus]

NO WAIT WAIT WAIT DID LEANDER ACTUALLY LIE THAT HE HAS SOME INFORMATION ON THE CURSE JUST TO GET US ALONEEEEEEEEEEEEEE

[lamaery]

8 - Design // SPOILERS for Rhythm of War and Yumi

Well, well, well … since I do have some lineart for the scene in which we are properly introduced to Design lying around on my shelved-project-shelf, I took the opportunity to try colour some bits of it. That cryptic is such a delight. I am sure she would have been brilliant at annoying Elhokar as well. But I guess Hoid kind of deserves her, too.