Adonis Diaries

Archive for May 25th, 2022

It’s really hard for someone who loves mathematics to get bored: maticians can play fun games …

ali.medium.com

You may think that we are unable to match natural numbers to rational numbers, and the density is enormous.

However, we can use one-to-one correspondence in all positive rational numbers.

Let us move forward using the image below. We wrote natural numbers going to infinity in the first row and column. Then, following a specific pattern, we wrote all rational numbers.

For example, first, we wrote all of the numerators as one and made it so that the denominators were getting larger.

We followed the same process except with two as the numerator in the next row. We then continue these steps to infinity. If we follow the below method for matching, we notice that one-to-one correspondence is, in fact, possible — 1 to 2, 2 to ½, ½ to ⅓, ⅓ to 3, etc.

Cantor’s diagonal argument

As you can see, we can match all natural numbers to positive rational numbers. If we wanted to, we could also use this logic to match all rational numbers to integers. Therefore, we can surmise that rational numbers are countable.

What about real numbers?

Real numbers are Not countable, and Cantor has provided very lovely proof for this as well.

When proving that real numbers are not countable, Cantor used the contradiction method to show that the interval between (0–1) is uncountably large.

First, he assumes that the distance between (0–1) is countable, and when he proves it wrong, he gets a contradiction.

First, Cantor writes all natural numbers from 1 to n, starting at the top left of an empty piece of paper he finds. He then assumes he writes all the numbers between (0–1) on their right, naming them as x₁, x₂, x₃, etc.1 → x₁ = 0.256173…
2 → x₂ = 0.654321…
3 → x₃ = 0.876241…
4 → x₄ = 0.60000…
5 → x₅ = 0.67678…
6 → x₆ = 0.38751…
. . . .
n → xₙ = 0.a₁a₂a₃a₄…aₙ…
. . . .

According to his first assumption, Cantor thinks he should not find any other number between (0–1). He also knows, however, that he must prove this mathematically. 

That is why he starts looking for a number he thinks is not between (0–1), b.

Using a straightforward approach, Cantor finds a number b. 
First of all, he takes the first number that he wrote x₁ and increases its first decimal place by one, and writes b in the first decimal place. 
Therefore he makes two into three and says b = 0.3….. He then says that b is different from x₁.

Then, he makes the second decimal place of x₂ one greater and writes b in the second decimal place. Therefore, he makes 5 into 6 and says that b = 0.36…. 
He then says that b is different than x₂.

Afterward, he raises the third decimal place of x₃ by one and puts b in place of the third decimal place. Therefore, 6 becomes 7, and he writes that b = 0.367…. He then says that the number b is different from x₃.

Cantor continues this pattern and finds a number between (0–1) different from all the numbers he has written before. He then accepts that his assumption is false.

Using the contradiction method, he surmises that real numbers are uncountable because many numbers are left unmatched when one-to-one correspondence is done.

He makes a note in history that real numbers are uncountable.

Cantor published this revolutionary proof in his article called Über eine elementere Frage der Mannigfaltigkeitslehre .’

In less mathematical terms, he would show the world what he had discovered while dealing with his friend’s question, the existence of infinite-element sets with different numbers of elements.

In even simpler terms, he said that “while both natural numbers and real number sets have an infinite number of objects, the real numbers set has more objects in it.”

There are many different kinds of Infinity...In which Infinity would you like to play the game?

The Palestinian Information Center 

Zakaria al-Zubaidi, Palestinian detainee and one of 6 prisoners who were recaptured after escaping Gilboa Prison last September, talks in his latest letter from prison.

Zakaria never got the chance to say goodbye to any of 4 family members he’s lost throughout the years. He was in prison when his father died in the 1980s. His mother and brother Taha were murdered by Israeli occupation forces in Jenin Invasion in 2002 and he couldn’t see them or hold funeral rituals.

Last week he lost another brother, Daoud, who was shot dead by Israeli forces in Jenin.

(Image via Eye on Palestine)

May be an image of 2 people and text that says 'EYE ON PALESTINE W ZAKARIA AL-ZUBAIDI "ALL THOSE I LOST, I DID NOT SAY GOODBYE TO THEM AND DID NOT BURY THEM"'

Adonis

May be an image of 2 people and text that says 'Palestine Online Petition details Comments Updates Support Scholars, Activists, and Journalists Facing Censorsh and Surveillance in Germany Letter in support of Dr. Anna- Esther Younes Nearly 500 500 prominent scholars, artists, activists and organizations support German-Palestinian scholar Dr. Anna Younes against censorship and anti-Palestinian racism in Germany'
500 prominent scholars, artists, activists and organizations have slammed the censorship and anti-Palestinian racism in Germany targeting Dr. Anna Younes, a German-Palestinian critical race and post-colonial scholar, stressing their solidarity with her.

Adonis

May be an image of 1 person and text that says 'Palestine Remembering Tom Hurndall On 11 April 2003, Israeli sniper shot Tom in the head while trying to rescue children from Israeli gunfire ine line in Gaza.'
On this day in 2003, an Israeli sniper shot British activist and journalist Tom Hurndall while attempting to rescue a child who had been pinned down by gunfire in Gaza Strip.
He died nine months later in hospital in London. He was 22.

Israel has a long history of sniping-dead Palestinians and foreign journalists, and Nisrine Abu Akilat will Not be the last one.

During the weekly demonstrations in Gaza on the border under the “Rights of Return”, scores of Palestinians and journalist were sniped-dead, and many were targeted to be handicapped for life, especially in the legs to prevent them from walking in massive marches again…

Adonis

May be an image of one or more people and text that says 'Palestine くぐ PHOTO ODAYDAIBES PHOTO:ODAYDAIBES DAY In a matter of hours, occupied West Bank bids farewell to 4 Palestinians murdered by Israeli gunfire'
In a matter of hours, 4 Palestinians, including 2 women, got murdered in cold blood by Israeli forces’ bullets in the occupied West Bank.

Because they NOT just Numbers,
Say Their Names:

1. Ghada Sabatin, 47
2. Maha Za’atari, 24
3. Muhammad Ghneim, 21
4. Muhammad Zakarneh, 17

Adonis

May be an image of standing, outdoors and text that says 'IMEU Chaque année à l'automne, juste quand les fermiers palestiniens se préparent a récolter leurs olives, des colons işraéliens attaquent violemment les oliviers et les fermiers palestiniens.'
Israel made it a strategy to cut down as many Olive tree as possible, on account this tree is a Symbol for survival of the Palestinian people.

Adonis

May be an image of 1 person, outdoors and text that says 'IMEU Les assauts sur es oliveraies palestiniennes par les colons israéliens un acte de guerre environnemental continuent de s'intensifier. ce jour, au moins 800 000 oliviers ont été déracinés à la tois par les autorités israéliennes et les colons.'
Israel settlers have uprooted more than 800,000 olive trees.

Adonis

May be an image of ‎one or more people, book and ‎text that says '‎HABIBI ليلة 3000NIGHTS 3000 NIGHTS Vitro ية الهد PRESENT salt سفتك sea HISTOIRES PALESTINIENNES Une sélection de 32 films palestiniens sur Netflix إجرين مارادونا MARADONA'LEGS GIRAFFADA DIVNE INTERVENTION LAVE‎'‎‎
Retrouvez la collection sur les “Histoires Palestiniennes” de Netflix dans cet article 👉 https://bit.ly/3aLS5RJ
May be an image of text that says '1. Le sel de la mer 2 A drowning man 3. Rêves d'exil 4. A man returned 5. When I saw you 6. Les enfants de Shatila 7. Intervention divine 8. The Crossing 9. Paradise now 10. Chronique d'une disparition 11. Maradona's legs 12 3000 nuits 13. In vitro 14. Bonboné 15. 15 Three Logical Exists 16 La chasse aux fantômes 17. Ave Maria'

adonis49

adonis49

adonis49

Blog Stats

  • 1,496,387 hits

Enter your email address to subscribe to this blog and receive notifications of new posts by email.adonisbouh@gmail.com

Join 821 other followers

%d bloggers like this: