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So has Parmenides , Shakespeare and the Sound of Music
If: x/x = 1 is true for all values of x

And: x/0 = infinity is true for all values of x

does 0/0 = 1 ?

or does 0/0 = infinity ?

or does 0/0 = 0 ?


That's where I got stuck, last time I tried.


It equals all values
Actually 0/0 cannot equal anything. It either has a distinct value or no value at all. The rules of equality dictate that a=b and a=c only if b=c. If 0/0 could equal anything then by this rule 0/0=1 and 0/0=2 implies 1=2.

0/0 makes sense only when you allow the concept of limits. Then the limit of x/y as x and y both approach 0 can be anything but is fixed by how x and y were originally defined.
I don't claim to be a mathematician but I think that is a wrong conclusion. 1 should not be seen as implying an equality with 2 from that. But that in some circumstances 1 would have the same effect as 2.
I reckon that implies, that the mathematicians need to go back and look at their basic rules as they seem inaccurately stated.
It is the right conclusion though. That is how equality is defined.
The definitions work well and behave as required. 0/0 does not have a value, and is not equal to anything.
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^^^^^ What The Funicular!!
Apologies for the sidetrack, Ratter!

I was going to add that the concept of dividing zero things into zero portions is just absurd.

Dividing a thing into an enormous number of portions necessitating microscopuc portions, yes that is fine.

Dividing a thing into less than 1 portion is, again, conceptually absurd. Everything on the 1/x graph between -1 and +1 is suspect, imho. And both + and - infinity are bang smack in the middle of that zone.




;)

Why should dividing a thing into less than one portion be any more absurd than dividing a thing into, say one portion and a bit?
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Ok, I'm lost here now!
You've been hijacked, Ratter. ;o)
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Oh!! Ok....
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It appears that way lol
Sorry about that, someone asked about infinity and I thought I'd answer and things have sort of snowballed really. Oh, well.
A big bang is simply the event horizon as observed from within a black hole.

Two to go ;o)
I prefer Kaley Cuoco to Melissa Rauch but would be happy with either.....

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