Ahh.. someone with at least a tiny bit of education...

alan1000 wrote:I'm not a mathematician so bear with my inexperience... but I don't think that anybody here has actually stipulated which definition of "0" they are working with?

If 0 is understood as a Robinson infinitesimal in non-standard analysis, then 2/0 does indeed equal infinity,

That could be true except to refer to hyperreal numbers requires that one use hyperreal notation or at very least specify such. A variety of hyperreal notations have been offered by pretty well known mathematicians. I have my own notation (for philosophical reasons). And another thing that is required, although unknown to many mathematicians, is logic. Mathematics is a subset of logic and cannot defy logic in its construction without becoming incoherent and useless.

alan1000 wrote:and 0/2 does indeed equal 0 (I think. I'm not pretending I understand non-standard analysis - I read about it in a book).

Again, if using proper notation, "0" is undefined because the "degree of 0" isn't being specified.

0.000...:000 / 2 would still be 0.000...:000

or my own notation:

[0.000...:0R] / 2 = [0.000...:0R]

{R == "eternally Remaining amount for sake of non-ending decimals"}.

alan1000 wrote:On the other hand, if 0 is considered as "the null set", the expression 0/2 is simply not admissible because the null set does not contain 2 subsets.

That is an excellent observation, although I would disagree with your logic.

One cannot divide 2 by a null set, because the statement itself makes no sense (hence is "undefined"). But

dividing nothing yields nothing, always. The number of parts requested is irrelevant. Thus;

0/2 = 0, just as standard analysis proposes.

alan1000 wrote:(In fact you might like to argue, just to be mischievous, that to be divisible by 2, the null set would have to contain three subsets - can you guess why?)

I am curious of your reasoning.

Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony ElseFrom THIS age of sleep, Homo-sapien shall never awake.The Wise gather together to help one another in EVERY aspect of living.You are always more insecure than you think, just not by what you think.The only absolute certainty is formed by the absolute lack of alternatives.It is not merely "

do what works", but "

to accomplish what purpose in what time frame at what cost".

As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.

Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "

The situation cannot be what it is and also remain as it is".

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