Now in a countable infinite set what is the state of "alef" when we take the set from 0 to minus infinity? What happens in the mapping then? Besides what if we count from minus to plus Infinity? What happens then?
What happens is one set is countably infinite and the other is uncountably infinite. That’s Cantor’s proof and he was the first to discover it. A genius.
Sir natural numbers start from 1...not from 0 .... there are the whole numbers start from 0...so can you tell me why u are saying such sets ...THE SET OF NATURAL NUMBERS???
Unfortunately, different branches of mathematics differ on whether 0 is a natural number. In branches of math like logic, set theory, combinatorics, and abstract algebra, 0 is often considered to be a natural number. It is better for these disciplines when 0 is included in the set of natural numbers. In branches of math which use analysis/calculus, 0 is often not considered to be a natural number. It is better for these disciplines when 0 is not in the set of natural numbers (since they often want to take reciprocals of natural numbers, and 0 doesn't have a reciprocal). So that's how things typically go. In set theory and computer science, 0 is almost always considered a natural number.
Zero is, together with one, the only "real" natural number. Everything else is mathematics and therefor abstractions. Either something is there, or it isn't. This requires an quantified space-time continuum though.
I've watched all of your videos and saw that they were good.
Finally!! I understood uncountably infinite set. It is very helpful. Thx
God damn it, I have to know this material in 4 days from now for my set theory final :'(
saaaaaaame exactly same for me rn lmao
How'd it go?
Your video gives me the hope to continue study mathematics. Thanks
godlike explanation.
thank you so much for this video! I finally understand uncountably infinite sets :D
Now in a countable infinite set what is the state of "alef" when we take the set from 0 to minus infinity? What happens in the mapping then? Besides what if we count from minus to plus Infinity? What happens then?
What happens is one set is countably infinite and the other is uncountably infinite. That’s Cantor’s proof and he was the first to discover it. A genius.
(-infinity, 0) can be map with ℕ⨯ℕ
By f(m,n)={-m/n : m∈ℕ, n∈ℕ}
And ℕ⨯ℕ is countably infinite set .
But it is only for set of rationals.
Thanks, man. Very helpful.
does the sequence have to be a 1 or 0 ? can it not takes any other values
They’re examples of countably and uncountably infinite sets. Cantor’s proof is the important thing not the examples of the sets chosen.
Sir natural numbers start from 1...not from 0 .... there are the whole numbers start from 0...so can you tell me why u are saying such sets ...THE SET OF NATURAL NUMBERS???
0 is a natural number. Integers don’t have a starting point.
@@paulu_ My book says they do start from 1. Why it has to be so confusing? Why isn't there a convention which states where N numbers starts from?
Unfortunately, different branches of mathematics differ on whether 0 is a natural number.
In branches of math like logic, set theory, combinatorics, and abstract algebra, 0 is often considered to be a natural number. It is better for these disciplines when 0 is included in the set of natural numbers.
In branches of math which use analysis/calculus, 0 is often not considered to be a natural number. It is better for these disciplines when 0 is not in the set of natural numbers (since they often want to take reciprocals of natural numbers, and 0 doesn't have a reciprocal).
So that's how things typically go. In set theory and computer science, 0 is almost always considered a natural number.
Where is the definition of cardinality?
Thanks
Very helpful
Hmm. I Don 't get it with the s'
I UNDERSTAND THANK YOU
very good
nice i want to learn that thing in high school thanks
Thanks!!!
ℵ0
adn please let me more about math cause i need in highschool ok
please
Excellent thank you sooo much
0 belongs to the set of whole numbers. The set natural numbers/counting numbers includes 1,2,3,4 etc.
No shit Sherlock
thanks dude
0 is not a natural number.
+Nakul Haridas This is highly debated in mathematics, and many see 0 as such.
zero is not a natural number :(
It's debated, some argue that 0 is a natural number and a fair amount of computer scientists tend to be on the side of 0 being a natural number.
Zero is, together with one, the only "real" natural number. Everything else is mathematics and therefor abstractions. Either something is there, or it isn't. This requires an quantified space-time continuum though.
in discrete math 0 is considered as a natural number
it is natural number
Thats like debating someones point because they had a grammar error in their argument.
0 is not a natural number. The set of natural numbers begins with 1.
It varies in maths, s0 no that’s not true