First you conceptually divorce quantity from substance (as if).
Then you extrapolate the quantity '0' (see log below)
Then you pretend that 0 is fundamentally as valid as any other number.

Then you divide by it to get its reciprocal, infinity, another quantity
 without any possible substance.

Infinity is a different type of 'quantity' from the quantities of physical,
 existent things.  For those quanties you can get from any quantity to any
 other quantity by successive addition.  (or subtraction).  For example,
 the mass of a paper clip vs. the mass of the known universe.
 But no matter how
 many units of mass I add to the mass of the paper clip, I will not reach an
 infinity quantity.  (you can add infinity, but that begs the question, and
 you can't measure an infinite quantity in the first place to justify it.
 And if it did have an infinite quantity, adding 5 to it would still give you
 the same infinity, so the quantity must be larger than itself (!)  (You could
 say the result is actually infinity + 5, but then you're giving a complex or
 2-dimensional quantity to a scalar value which had hitherto been defined
 using 1-dimensional quantities.))
 "You can so measure an infinite quantity.  Take the ohmmeter for example."
 The ohmmeter is not measuring an infinite quantity when it reports infinite
 ohms.  What it actually measures is how much electricity passes from one
 node to the other.  If electricity does not pass from one node to the other
 (or not enough passes for it to detect), it takes the reciprocal of
 "0 electricity" and derives "infinite ohms". ("undefined" may be more
 accurate (but less practical since "undefined" doesn't necessarily imply
 "no electricity."))

10 apples = 0 oranges, 6 pears = 0 oranges, therefore 10 apples = 6 pears


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<neg1> 1+1=2
<asadasAFK> 1-1 = superfluous
<neg1> lol
<BALAGUER> 1-1=0
<asadasAFK> 0 = superfluous. :)


<SchzSoph0> "Zero" and "negative" numbers demonstrate that numbers are an invention... 
            "imaginary" and "complex" numbers make this even more striking
<asadasafa> SchzSoph0 i see the ordinal numbers as being more "real" than 0, etc.
<HotSpur> asadasafa you don't think 0 is real?
<asadasafa> hotspur : no, you never have 0 quantity of anything.
<asadasafa> to say there are zero apples is simply to say there is not an apple
<asadasafa> it's like a perverted way of saying it
<asadasafa> it's pretending there are apples
<asadasafa> and then trying to figure out, okay, if there are apples there (which there aren't), 
            then how many are there?
<SchzSoph0> asadasafa, that is the typical view, that the "Natural" numbers are "more real" than
            the rest of them.  But *mathematically*, they're indistinguishable.  "Natural" 
            Numbers are just easier to apply to the real world... "negative three" is hard to 
            apply to a pizza.
<asadasafa> it must be 1 minus 1!  brilliant! i'll call that zero!
<HotSpur> asadasafa as someone mentioned, the idea of zero was a fairly long time in coming. I 
          guess before zero, people just lost interest when there was none of something around.
<asadasafa> hotspur: or didnt have any particular need to quantify something that wasn't there. :)