Oh, come on. You are just being obtuse. This limitation of cardinality is exactly the same as the limitation velocity has in its inability to distinguish color.
Sheesh. I mean really!
No jsfisher, you simply ignore
http://www.internationalskeptics.com/forums/showpost.php?p=4989496&postcount=5618 .
You can always limit Cardinality in any way you like, but at the moment that some limitation is considered as the general case, forgery gets on stage.
This forgery can be found right at the foundations of Standard Math, and as a result Standard Math is not The Mathematical Science.
The cardinality of {} (notated as |{}|) is 0 exactly because we do not count the empty set as its own member.
So is the case with _____ ; we do not count it as its own building-block, exactly as {} is not its own member, but it does not mean that {} does not exist, and so is the case about ____
On the contrary, {} exists independently of the existence of members and its cardinality is exactly
∞.
Furthermore this independent existence is notated exactly by the outer "{" "}" of any given set, whether it is empty or not, and I call this existence Non-locality or non-local atom.
On top of this non-local atomic state we research the difference between the amounts of finite or non-finite elements.
An amount of finite elements along ______ has a well-known cardinality.
An amount of non-finite elements along ______ does not have a well-known cardinality, exactly because a non-local atom cannot fully be covered by non-finite amount of elements.
If we wish to avoid the measurement of Complexity, we simply reduce the existence of members to the minimal possible existence that is not nothingness (which is exactly a 0-dim element), so in both cases (the finite case and the non-finite case) we are using the minimal case of existing elements in order to get valid conclusions about the difference between finite cardinality and non-finite cardinality.
No amount of members (whether they are complex or not) has
∞ and this notion is beyond Standard Math's framework exactly because this framework can't deal with total-existence knownn also as non-locality, non-local atom, non-local atomic state (which is the opposite of nothingness), that is notated as "___" or as the outer "{" "}".
But if "{" "}" is used to notate a limit domain, then non-locality is also notated as "{_
}_"
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Jsfisher it is easy to demonstrate both your hypocrisy and your arbitrary limitation style, in this case:
Your hypocrisy:
You are the one that claims that fundamentals must not be limited to any particular case, as clearly shown in
http://www.internationalskeptics.com/forums/showpost.php?p=4858227&postcount=4197 . You did a great job by this post, which enabled me to unleash Organic Numbers form some limited representation of them.
But when I do the same thing to Cardinality, you are using an opposite attitude that is actually based on arbitrary limitations.
Your arbitrary limitation style can be shown by using exactly the same subject:
Your arbitrary limitation style:
In
http://www.internationalskeptics.com/forums/showpost.php?p=4859147&postcount=4199 I understand your extension of Organic Numbers representation, and ask you about further extensions that are based also on Redundancy-only cases.
Here is your answer, which is based on your arbitrary limitation style:
http://www.internationalskeptics.com/forums/showpost.php?p=4859277&postcount=4201
You have no clue what Distinction is but you have no problems to argue about it.
Say no more.
