A Set Theory for Scientists and Engineers

[tommyrjensen]

There is already a set aleph_1 used in ZF, it is defined as the set of all countable ordinals. It is clearly not the same as the combinatorial set of aleph_0, since every finite ordinal is an element of aleph_1 but not of the combinatorial set of aleph_0. So what does your ACS really mean? It looks like you want to use the same name for two altogether different sets.

[tommyrjensen]

It is easy to prove in ZF that the unit interval is an uncountable set. Thus if you add AI to ZF you apparently get an inconsistent theory. It does not seem of much value then.

[Dzikslol]

Thumbs up for Bach

[Gargonzolo]

@Dzikslol thumbs down for MIDI

[CHistrue]

In my video's (please view), I presented an elementary philosophical argument as to why I believe that the Continuum Hypothesis is correct. My main axiom is the notion that levels of Infinity higher than Aleph Nought are not bound by discreet binary reality, and thus that they cannot be multiplied by zero in any real sense. Calculus=limits, but "thing-in-itself" transcends limits. Cantor was correct in his insights, I believe, making Calculus a reality on one level transcended on another.

[ahhhhjjjj]

@CHistrue You sounded like the Nietzsche of Mathematics there for a second. Hahaha. Just teasing :P

[Muffinman10123]

Also, the combinatorial set axiom seems to follow logically from the axiom of power set...

[kautilya33]

Cardinalities of the combinatorial and powerset are the same, but the combinatorial axiom does not follow from the powerset axiom. For more details, type "intuitive set theory" without quotes in google search box.

[Muffinman10123]

Hmm. I thought that bonded sacks, which have figments as its elements, are defined by the fact that they cannot have elements picked by the axiom of choice. I am new to set theory and all of these concepts in general, sorry..

[kautilya33]

IST merely defines and introduces the notion of a bonded sack with untouchable figments in it, and in no way interferes with the elements of ZF theory and the axiom of choice.

[Muffinman10123]

This omits the Axiom of Choice?

[kautilya33]

Axiom of Choice is very much part of IST. It can choose any element from a set containing infinitesimals and figments.