- #1

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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