Russell’s Paradox

Math’s new controversy? Could this even be possible?!

Darth Vader Laughing

“At last the Force has pompously shown its repulsiveness!… Muahahah…”

We’re back again for another excessively interesting theme today! In fact, many scientists, including applied mathematicians and science theorists, claim that even though there are 2 general resolutions for this so called ‘antimony’ , it still remains unveiled.

So let’s get started with the statements, and finally observe, whether we’re talking Mystery or History.

Jay-Z

Hit the beat Jay! You’re tunin’ it today


Biography goes first

Bertrand Russell photo

Bertrand Russell (1872-1970)

According to britannica.com:

Bertrand Russell, in full Bertrand Arthur William Russell, 3rd Earl Russell of Kingston Russell, Viscount Amberley of Amberley and of Ardsalla, (born May 18, 1872, Trelleck, Monmouthshire, Wales—died February 2, 1970, Penrhyndeudraeth, Merioneth), British philosopher, logician, and social reformer, founding figure in the analytic movement in Anglo-American philosophy, and recipient of the Nobel Prize for Literature in 1950.

 

Russell’s contributions to logicepistemology, and the philosophy of mathematics established him as one of the foremost philosophers of the 20th century. To the general public, however, he was best known as a campaigner for peace and as a popular writer on social, political, and moral subjects.

Hm… the Philosophy of mathematics… ‘Analytic movement’… Moral Subjects… all equal a mind-blowing concept in Math’s hierarchy of “Dignity and beyond”?!? Sounds compatible when it isn’t, and not compatible when it is, right? Don’t worry you’ll get what I mean by the end of this article… If we ever get there… Surmounting an infinite loop of questions and diversity… Or shall I saw Eternity…

Alright, enough of poetry, let’s get to those FACTS.


 

#imaginationlandiastangolia, another jammed term of mine for   “the land of sophisticated logic”

#1

Imagine you had an empty box.

Seems simplistic, doesn’t it?

#2

Now, let us put some of nature’s masterpieces–an apple and orange–into the box.

What do we have now? No, not a receipt of 50,000 so’ms (#joke-insiders), but rather a set, mathematically speaking.

#3

Now, say you had to think about your friend’s mother’s son and you decided to add another fruit.

The irony is that, mathematically, NOTHING CHANGES!

Alluding to the definition: “A set is a collection of distinct objects, considered as an entity unto itself”, things get weird already.

#4

Alright, check point mate. We’re almost there.

In this case, the process of addition may be applied infinite times, so that:

A box could be in a box, with a box in which the box that had been inserted in has another box  deployed in another one.

And the process goes on and on and on… Please greet the infinity loop-deloop!

#5

A virtual student: “Speaking of boxes and sets, does it turn out that the Box with the 2 fruit inserted in the overall set can contain itself in an overall set?”

Good question. Not necessarily.

The outer box contains an Apple, an Orange and the Box with both of the previous inside. Yet, the inner box only has 2 objects: the Apple and Orange

It’s missing its own box inside, to fulfill the set.

Hence, when we try to add another one, we come across the same problem!


There is still an analogous explanation!

This is more of the classical version of explanatory towards this Paradox, albeit I found the Box Mystery more convenient to deliver.


 

resolution:

After these findings, scholars and scientists began to think that there was something lying in the depth of unknown mathematics, that leads us to this ‘incomplete’ set theory.

However, mathematicians never stop on what they do, so 2 resolutions regarding to this problem have been published ever since.

The Naive Set Theory 

and

The Set Theory


so the sets lived happily ever after!

Thanks for reading my article!

If you have any suggestions, you know what to do. *wink*

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Written by Shohruh Artaman
A typical writer illustrating typical principles
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  1. Supercalifragilisticexpialadocious! Very well explained with great sophistication and analytically well organized manner

    Reply
    • Thanks a lot, it’s great to hear people understand your content!

      Reply

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