**Frog( 1 ) NOT = Dog( 0.9999...)--zero( 0 ) NOT = 0.111....**
rr6....Yeah RP, this the key point--- called mapping ---where Column X with n becomes a in Column Y with a etc....again this at first sight and with minimal knowledge of what will appear to most humans, as complex branch mathematics, that, is changing X-n( frog ) into Y-a( dog ) i.e. to me all of this still leads to what is obvious to most humans who would view the original statements again;

You have failed to give us a relatively simple, rational logical and understandable to the average human, within this one email message with ingecti, surjectives etc, o whatever alien terms....thx again, but no banana for you RP.

rational finite( 1 ) does not equal irrational infinite 0.999 .....

non-counting( 0 ) does not equal irrational infinite 0.111....

Space = macro-micro infinite

..micro = >IN<--subdividing space INward--multiplication-by-division

..macro = <OUT>--addition-by-radial expansion outward

0 = non-counting number

0 is representative of macro-micro infinite non-occupied space beyond our finite

__occupied space__
0 = empty column on abacus.

0.111....does not equal zero( 0 )

0.999.....does not equal one( 1 )

Inifinity is irrational concept except in relationship to infinite space.

Space

..1a) non-occupied and macro-micro infinite, embraces;

..1b)

__occupied space__...

Mathematics represent values associated with;

1) finite

__occupied space__,

2) infinite non-occupied space,

3) imaginary concepts of mind, that may or may not directly correlate to either of the latter #2 and #1 above.

Rational does not equal irrational.

Irrational values are expressed using numerical symbols similar to rational values being expressed using numerical symbols.

The irrationally infinite, macro-micro infinite non-occuped space, that embraces our finite Universe of

__occupied space__ may be the only exception to our mathematical rules, as that is the only time we can correlate to an infinite value existence.

Who values the irrelevant non-occupied space( 0 ) that exists beyond our finite

__occupied space__( 1 )

**Uni**verse?

The non-occupied space exists purely as a infinite reference set of zero representated value/non-point(s) having being of no immediate value to humans, other than as the most cosmic refersence set( infinite ) for our finite

**Uni**verse.

Fuller believed in the possibility of micro-infinite subdivision of our finite

__occupied space__ **Uni**verse i.e. eternal increase of quanta via micro-infinite multiplicaiton-by-division of our finite **Uni**verse of__ occupied space__.

I dont believe so. The graviton is the cosmic minimal limit. Does the graviton have variable limits? Didn't L. Smolin suggest such on the ultra-micro scale and on a ultra-macro cosmological scale of Universe that expands to varying radial values at differrent times of expansion-contraction?

r6