- #1
Doron Shadmi
Because by Conventional-Mathematics, every R member is a point in the Real-line, then:
{.} = any non-empty R member
|{}| = The cardinality of the empty set = 0
|{.}| = The smallest catdinality of any non-empty set = 1
0 or 1 are members of W.
Between 0 to 1 there is {} or in other words, the transition from
0 to 1 and vice versa, is a phase transition or a quantum leap.
The transition's type from {} to {.} = the transition's type from 0 to 1 but,
because it is a phase transition, and we cannot use {} or {.}
as an element between {} to {.}, we have no choice but to
define a new set's content.
{} = Emptiness
{.}= Localized element = Point
{_}= Non-localized element = Line
Therefore between {} to {.} there is {_}.
Now we can conclude that between any two non-empty R members there
exist a non-localized element.
Therefore |R| does not have the power of the Continuum.
{.} = any non-empty R member
|{}| = The cardinality of the empty set = 0
|{.}| = The smallest catdinality of any non-empty set = 1
0 or 1 are members of W.
Between 0 to 1 there is {} or in other words, the transition from
0 to 1 and vice versa, is a phase transition or a quantum leap.
The transition's type from {} to {.} = the transition's type from 0 to 1 but,
because it is a phase transition, and we cannot use {} or {.}
as an element between {} to {.}, we have no choice but to
define a new set's content.
{} = Emptiness
{.}= Localized element = Point
{_}= Non-localized element = Line
Therefore between {} to {.} there is {_}.
Now we can conclude that between any two non-empty R members there
exist a non-localized element.
Therefore |R| does not have the power of the Continuum.
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