I do a detailed analysis of Cantor’s theory of uncountable sets. The logic of his proofs has some weaknesses. I propose an axiom and a solution to continuum hypothesis. The main idea is: Assumption of Cantor’s proofs: All real numbers (set R) are in a list (list L). This assumption means R=L, considering L as...

An analysis of Cantor’s theory of uncountable sets: The logic of his proofs has some weaknesses. Cantor assumes for both his proofs that all real numbers (set R) are in a list (list L). Considering L as a set this assumption assumes R belongs to L. This makes the claim “a real number is constructed...

Cantor’s diagonal argument claims that ℝ is uncountable. When we see real numbers as points on the number line, we can put a name on each point and put the names into a list without contravening Cantor’s diagonal argument because we cannot create a diagonal from a list of names. However, we do not need...

The roll, pitch and yaw of an object relative to another is complex to compute. We use 3D complex number to compute them which makes the computation easier and more intuitive. Roll, pitch and yaw are angles of orientation of an object in space and the conversion of these angles among different reference frames is...

The apparent non‑gravitational acceleration the extra-solar-system ‘Oumuamua exhibits is puzzling. We find that when the position and velocity of the Sun is correctly set in computing the predicted orbit, ‘Oumuamua’s trajectory can be explained with gravity and we have reproduced the unexpected gap by computation. We also propose to search for new extra-solar-system high speed...

This is one of those portraits generated by Midjourney, not that of a real person.Like many people I’m impressed with the facility of Midjourney to create portraits of photogenic people. But how attractive or engaging would a person Iike this seem to be to you if you are someone, as I am, who struggled to...

Hilbert’s Grand Hotel shows that a fully occupied hotel with infinitely many rooms can accommodate additional guests. But our analyze finds that this is not true. Let us illustrate Hilbert’s Grand Hotel in Figure 1 where each square is a room and is occupied. Suppose that the rooms of the hotel are numbered 1, 2,...

Abstract: The Lorentz force law is fundamental for electromagnetism. However, it is known long ago that the Lorentz forces between two current elements do not respect the Newton’s third law. This seemingly harmless flaw had never been corrected. In physical sciences a discrepancy often hides in it new understanding or unexpected breakthrough. For solving this...

« N-complex number, N-dimensional polar coordinate and 4D Klein bottle with 4-complex number» “A concrete representation of a 4D Klein bottle has been desired by many but has never been presented. So, I decided to dive into the Klein bottle. Working with the Klein bottle was my first opportunity to practice with this system. To...

We've bought our first home, and we are so excited to remodel the kitchen! We're keeping our updates simple and on a budget, but the imact will be HUGE!

The post Mini Kitchen Remodel – The “Before” – Virginia Beach, VA appeared first on Joyful Abode.

Looking for the simplest Waldorf kite paper star pattern? You’ve found it! Anyone can make a beautiful sun catcher for their window out of translucent paper. This pattern gives young children the delight of creating their own decoration, while practicing fine motor skills. Please note though – it may be a bit tricky for kids […]

The post The Simplest Waldorf Star Pattern – Beautiful and Easy Decoration appeared first on Joyful Abode.

This post may contain affiliate links. If you make a purchase through an affiliate link, the site author may receive a small commission. The mini kitchen remodel reveal Have you been on the edge of your seat, wondering how my DIY mini kitchen remodel turned out? Well, here we go! We didn’t do a full […]

The post Mini Kitchen Remodel – Bright & Airy AFTER (You’ll love it!) appeared first on Joyful Abode.

A travel guide for moms who are traveling alone. It can be hard to find time to do things for yourself when you have young kids at home, so why not take advantage of the opportunity to travel without them? Here are some great ideas for your next solo momcation.

The post 9 Tips for Your Best Momcation – How to Maximize your Relaxation appeared first on Joyful Abode.

By Leo Babauta Let’s imagine that there’s a big task you’ve been avoiding for weeks (or maybe a bunch of them!) … it just becomes this ball of dread that you don’t want to think about, but that you feel really bad that you’ve been putting off. Sound familiar? Everyone has something like this, whether […]

The post Turning Towards a Task You’ve Been Avoiding for Weeks appeared first on zen habits.

By Leo Babauta When we’re looking to grow, what we’re really trying to do is step into a new, expanded view of ourselves. For example, if you want to be more mindful, or live more simply, or be more compassionate with yourself or others, or be more disciplined about your meaningful work … these are […]

The post Expanding Beyond Our Old Self-View appeared first on zen habits.

By Leo Babauta There’s a practice that I find to be really valuable, and I call it “Examining Beliefs.” If you regularly engage with this, it will transform you. Let’s say there’s something you want to do but you feel stuck — maybe you’re procrastinating a lot, maybe you’re stuck in an old habit. The […]

The post The Practice of Examining Our Beliefs appeared first on zen habits.

By Leo Babauta I believe in finding powerful practices for transformation wherever we can find them. And the Stoic philosophers Epictetus, Marcus Aurelius, Seneca are huge inspirations for me. I’ve found there to be a huge overlap between Stoicism and Zen Buddhism, even if there are also some key differences. The overlap between Zen & […]

The post 5 Stoic & Zen Practices That I Believe In appeared first on zen habits.

The internet went crazy today when a rumor seemed to break through about the always-destined Harry Potter television show — specifically that while no series is actually in the works, WB is now officially shopping for writers and pitches for an HBO Max event. We did a quick-and-dirty reaction pod with our three hosts and our good friend Proma Khosla, a longtime LeakyCon staffer and Mashable entertainment reporter, to break down the news, what it means for the franchise, and what the fandom does now. 

Basically, we decided the fandom just needs to get a trillion dollars together and buy the franchise from JKR. 

You can follow Proma on Twitter at @promawhatup  and read her Mashable articles here!

~*~

Don't forget to follow us on @pottercast on Twitter and @pottercastpod on Instagram!

Join our patreon! patreon.com/pottercast - Now, you can also join our Discord community there!

You can also buy PotterCast-related merch at mischiefmerch.com!

Happy 2022 and welcome to season 17! This one was recorded a little bit ago, when we got the title of the next Potter movie, but it's chock full of theories and ideas about what could be coming in the third movie. More soon!

We are still going through your emails for guest hosts! Also, we are still looking for editors so if that's you email us at staff@pottercast.com!

Don't forget to follow us on @pottercast on Twitter and @pottercastpod on Instagram!

Join our patreon! patreon.com/pottercast - Now, you can also join our Discord community there!

You can also buy PotterCast-related merch at mischiefmerch.com!

This episode was produced by Christine Peruski. Hosts Melissa Anelli, Frank Franco, and John Noe. PotterCast is (c) PotterCast 2005-2021.

We haven't seen it yet, but we've seen all the trailers and we have THOUGHTS. John, Frak, and Melissa discuss the "Fantastic Beasts: Secrets of Dumbledore" revelations — like the fact that it's almost certainly the last one.

~*~

Don't forget to follow us on @pottercast on Twitter and @pottercastpod on Instagram!

Join our patreon! patreon.com/pottercast - Now, you can also join our Discord community there!

You can also buy PotterCast-related merch at mischiefmerch.com!

This episode was produced by Melissa Anelli. Hosts Melissa Anelli, Frank Franco, and John Noe. PotterCast is (c) PotterCast 2005-2022.

WARNING: Volume. RIP headphone users.

We've featured the work of Ray Villafane before here on WIN, but today we have another of the pumpkin sculptures that made him famous. This time, it's his largest piece ever, unveiled at the New York Botanical gardens this last weekend. The piece is made of several pumpkins, with different sections carved and then held together with rods and adhesive. Check for more in the gallery below!

What even is this planet that we live on anymore though?

It turns out that there's a VERY fine line between Donald Trump and the Futurama character Zapp Brannigan. Memes with Zapp's image and Trumps tweets started circulating the internet and they caught the attention of Billy West, the voice actor who plays Zapp Brannigan on Futurama. The recordings he made are out of this world.

It's every cat's greatest dream to finally catch that red dot. And sometimes they do (meaning we get tired of holding down the laser and pointing). 

There's plenty more fun with pets and animals over at Animal Captions!

The arm was created by Enabling the Future, which has a chapter at Sienna College in Albany, New York. For its first project the Siena e-NABLE group made an Iron Man-themed hand for 5-year-old Jack Carder in Ohio.



In this case, nine-year-old Karissa Mitchell's (who was born without a right hand and most of her wrist) mother reached out to the group on campus, Siena College's director of marketing and communications said.

"She's watched the movie at least 100 times. We sing the songs all the time. We even have a karaoke machine that's 'Frozen'-themed," said Karissa's mother. The prosthetic was built using a 3-D printer and is comprised of 30 parts (it took near 30 hours to make).

To help Karissa achieve her dream of becoming a Disney princess, the team used "a pretty transparent ice blue color filament and added snowflakes to the forearm and her name with an Elsa crown on the cuff," said Alyx Gleason, the project lead and president of Siera e-NABLE. The arm also came with an Olaf LED light source.

Anyone who is in need of an arm or hand is encouraged to reach out to Siena e-NABLE.

The action really picks up around the thirty second mark.

Respect for Badminton: +1

Uhuru Houston was born in Brooklyn in 1969. He joined the Port Authority of New York and New Jersey Police Department in 1993, and three years later married Sonya, whom he had met when they were both students at Norfolk State University. In 1999, he was assigned to the World Trade Center. On the morning

When he wrote this letter to his mother in 1944, Roald Dahl was working at the British Embassy in Washington, D.C.—one of hundreds of undercover agents employed by Britain’s MI6 foreign intelligence service to spy on the United States. Dahl’s debut novel, The Gremlins, had been published the year before, and it would be another

Although they only existed for seven years and released just three albums, Nirvana were a band of immeasurable influence in the music world thanks in no small part to Smells Like Teen Spirit, a single track on Nevermind, their second album. It was this song that brought them out into the open, going on to sell millions

I wrote this in the newsletter about this one… It’s an especially horrible issue, but one I’m intensely proud of. It’s one of those rare books that I think may actually be unique for its genre, and the logical end point of the line of thinking that’s run through all my work in superheroes. Namely, […]

One book out today, being Uber Invasion 3, which is probably the most classically Uber issue I’ve dropped, being primarily focused on a single battle engagement.  Available from your local shop, or Comixology.

Last week, I briefly mentioned the shaded metallic thread sets from Au Ver a Soie that I’m so happy to …

Today, we’re going to finish up the embroidery on the sample leaf for Harvest Hues. If you’re just joining in, …

Yesterday, we began the finishing process on Harvest Hues, and today, we are going to tie up the project! In …