Get Help And Discuss STEM Concepts From Math To Data Science & Financial Literacy
STEM Gender Equality | Join us on ZOOM | Spreading Mathematical Happiness

MathsGee is free of annoying ads. We want to keep it like this. You can help with your DONATION

1 like 0 dislike

What is $\aleph$  in mathematics?

in A Level Maths by Bronze Status (8,600 points) | 112 views

1 Answer

1 like 0 dislike
Best answer
Aleph is a letter from the Hebrew alphabet. Georg Cantor, a deeply religious man, introduced it to denote cardinalities of sets in his effort to provide a rigorous axiomatization of set theory.

Two of the results of Cantor's work appear paradoxical.

The first paradox has to do with Aleph-0 - the cardinality of all countably infinite sets: Although the sets N, Z and Q are strict subsets of each other, they all have the same cardinality i.e. Aleph-0.

The second paradox has to do with Aleph-1 - the cardinality of R (or just the interval [0, 1]), which is equal to the cardinality of the set of all subsets of Z i.e. 2 to the power Aleph-0.

It appears that the continuum hypothesis (CH - Hilbert 1st Problem)  that speculates on the existence of an infinite between Aleph-0 and Aleph-1, is quite independent of Axioms chosen for Axiomatisation of Set theory (e.g. Zermelo-Frankel + Axiom of choice). CH is thus an example of Godel Incompleteness Theorem: A statement that is neither provable nor disprovable.
by (45 points)
selected by

Related questions

0 like 0 dislike
1 answer
asked Mar 22, 2019 in A Level Maths by Tedsf Diamond (50,514 points) | 28 views

Welcome to MathsGee Q&A Bank, Africa’s largest personalized STEM and Financial Literacy education network that helps people find answers to problems, connect with others and take action to improve their outcomes.

MathsGee Q&A is the STEM and Financial Literacy knowledge-sharing community where students and experts put their heads together to crack their toughest questions.


Enter your email address:

11,552 questions
9,430 answers
10,405 users