In the first 40 seconds you manage to not only misstate Russell’s Paradox but also call something a paradox which isn’t a paradox at all. Also, Russell’s paradox isn’t “unsolved.” It meant we had to formally settle the axioms of set theory to avoid paradoxes like Russell’s.
@@in2infinitygeometry That is pretty much exactly what happened. But saying "merely" is unfair. We get to pick our axioms. That's why they're called axioms. Mathematicians decided that the existence of Russell's paradox meant they needed a better definition of a set, which they then created. That's just what math is.
I know most of the views on these videos are people with some level of maths understanding hatewatching this or enjoying the parody, but if this is your first introduction to RusselL's paradox please go and read about it somewhere else e.g. the wikipedia page. What this person is describing has nothing to do with Russell's paradox. 10/10 bit though
This is the introduction to solving the nature of infinity. The nature of 'folding' number space is also expressed in higher dimensional forms such as the 4D hypercube. When it rotates the part that is contained within the set (outer cube) swaps places. Thus it is both inside the set and outside at the same time, as it is a 4d mathematical object. Here we express a simplified solution based on a 2D square. More info in our article in2infinity.com/solving-infinity/
@@in2infinitygeometry how come you're article is the only one in the world stating that information? could it be that you're truly so narcissistic you believe you're right while everyone else is wrong?
@@in2infinitygeometry Stop spreading your bullshit on the internet. Nobody should be exposed to all your mad delusions, some people are not able to call your shit out, and end up believing it. I will report this channel to youtube to get it shut down. It should be a crime to post the video's you are producing. I'm MSc mathematics, so I know what I'm talking about. You don't even know what Russell's paradox is! WTF!
Please do more videos like these, this is just hillarious😂😂😂. You should talk to terrence howard, possibly collaborate with him and make some more hillarious content like this so that all of the mathematicians out there can have a good laugh. 😂😂
If X is any set, either X e X or X ~e X. That is, X contains itself or X does not contain itself. Now, we let R be the set of all set that do not contain themselves. R = Y | Y ~e Y. We then ask does R contain itself? Suppose R e R, so R contains itself. But R is the set of non-self-contained sets, R ~e R. This is a contradiction, so we must have ~( R e R ) which is the same as R ~e R! This say R does not contain itself. However if R ~e R, then non- self-contained. Since R is the set of all non-self-contained sets. We must have R e R. But, that is a contradiction also! So, if we assume either R is self-contained or R is non-self-contained, then we get a contradiction. This R is a problem set that cannot exist. The resolution to this paradox is to carefully “define” which sets can and cannot exist via Axioms of Set Theory. If you have any question feel free to ask me.
Actually Russell’s Class is a thing. It is simple the Class of all Sets that do not contain themselves. However, in standard Set Theory, it is not a set. We showed that above. Here more examples. The Class of All Sets is NOT a set. Suppose it is a set, and call it S. In Set Theory we can take amy set and add some element not that set. Let T S U {S}. T is everything in S and the set containing S. We can show that the set T is not in S. Therefore, S does not contain all sets, namely T. Therefore S is not a set. That was a little hand-waved, but I hope you get it. Here’s another. A singleton set is a set that contains exactly one element. The class of all singleton sets is not a set. When we think we have it pinned down to set R, we can add the singleton {R} to it and have a new set, Q. We can keep doing this, so the set of all singletons has now precise size. In set theory every set must have an exact size which is called it’s Cardinality. I’m not just saying that the class is just infinite. I’m saying it is bigger than any infinity. In set theory there are many sizes off infinity. There is a whole class of them.
In the first 40 seconds you manage to not only misstate Russell’s Paradox but also call something a paradox which isn’t a paradox at all. Also, Russell’s paradox isn’t “unsolved.” It meant we had to formally settle the axioms of set theory to avoid paradoxes like Russell’s.
I think modern mathematics is merely managed to navigate his way around the Russell paradox by inventing an axiomatic system that suits itself
I believe that modern mathematics has had to invent his way around the Russell paradox rather than dealing with the issue
@@in2infinitygeometry That is pretty much exactly what happened. But saying "merely" is unfair. We get to pick our axioms. That's why they're called axioms. Mathematicians decided that the existence of Russell's paradox meant they needed a better definition of a set, which they then created. That's just what math is.
If you look up the Russell (two l's) paradox on Wikipedia, you'll learn what it is.
Thanks, I updated the text.
@@in2infinitygeometry Yes but you still don't know what the Russell paradox is.
I know most of the views on these videos are people with some level of maths understanding hatewatching this or enjoying the parody, but if this is your first introduction to RusselL's paradox please go and read about it somewhere else e.g. the wikipedia page. What this person is describing has nothing to do with Russell's paradox. 10/10 bit though
This is Satire, right? Right?!
This is the introduction to solving the nature of infinity. The nature of 'folding' number space is also expressed in higher dimensional forms such as the 4D hypercube. When it rotates the part that is contained within the set (outer cube) swaps places. Thus it is both inside the set and outside at the same time, as it is a 4d mathematical object. Here we express a simplified solution based on a 2D square. More info in our article in2infinity.com/solving-infinity/
@@in2infinitygeometry how come you're article is the only one in the world stating that information? could it be that you're truly so narcissistic you believe you're right while everyone else is wrong?
You are a CRANK!!!!!! You re spreading misinformation. This site should be taken down.
@@in2infinitygeometry Stop spreading your bullshit on the internet. Nobody should be exposed to all your mad delusions, some people are not able to call your shit out, and end up believing it. I will report this channel to youtube to get it shut down. It should be a crime to post the video's you are producing. I'm MSc mathematics, so I know what I'm talking about. You don't even know what Russell's paradox is! WTF!
Please do more videos like these, this is just hillarious😂😂😂. You should talk to terrence howard, possibly collaborate with him and make some more hillarious content like this so that all of the mathematicians out there can have a good laugh. 😂😂
The russell paradox has literally nothing to do with numbers
At its core the Russell paradox could be explained mathematically is 1 over x = x
@@in2infinitygeometry Just so we're clear, can you tell me _exactly_ what you think the Russell paradox is?
@@in2infinitygeometry Stop yourself!!! Everything you do on in2infinity is totally bullshit. Remember to take your medication.
pretty much sure russell's paradox has to do with sets containing themselves... tf is this dude talking about
Yes ma’am you’re correct.
If X is any set, either X e X or X ~e X. That is, X contains itself or X does not contain itself. Now, we let R be the set of all set that do not contain themselves.
R = Y | Y ~e Y.
We then ask does R contain itself?
Suppose R e R, so R contains itself. But R is the set of non-self-contained sets, R ~e R. This is a contradiction, so we must have
~( R e R ) which is the same as
R ~e R! This say R does not contain itself.
However if R ~e R, then non- self-contained. Since R is the set of all non-self-contained sets. We must have R e R. But, that is a contradiction also!
So, if we assume either R is self-contained or R is non-self-contained, then we get a contradiction. This R is a problem set that cannot exist.
The resolution to this paradox is to carefully “define” which sets can and cannot exist via Axioms of Set Theory.
If you have any question feel free to ask me.
@@harveybernstein9203 If I’m correct, the concept of class can contain itself then what about russel paradox in this case ?
@@harveybernstein9203 heard about class when studying category theory btw and always wondered exactly what was a class and how it was define via ZFC
Actually Russell’s Class is a thing. It is simple the Class of all Sets that do not contain themselves. However, in standard Set Theory, it is not a set. We showed that above.
Here more examples. The Class of All Sets is NOT a set. Suppose it is a set, and call it S. In Set Theory we can take amy set and add some element not that set. Let T S U {S}. T is everything in S and the set containing S. We can show that the set T is not in S. Therefore, S does not contain all sets, namely T. Therefore S is not a set. That was a little hand-waved, but I hope you get it.
Here’s another. A singleton set is a set that contains exactly one element. The class of all singleton sets is not a set. When we think we have it pinned down to set R, we can add the singleton {R} to it and have a new set, Q. We can keep doing this, so the set of all singletons has now precise size. In set theory every set must have an exact size which is called it’s Cardinality.
I’m not just saying that the class is just infinite. I’m saying it is bigger than any infinity. In set theory there are many sizes off infinity. There is a whole class of them.
facts
It's Russell...
Thanks text updated
There are so many mistakes in these videos. It a shame.
If you wish for a fuller response, please indicate the mistakes. Thanks for your comment.
No
Yes
@@in2infinitygeometry touché
blood doesnt know what he's talking about
Feel free to elaborate your view