First you conceptually divorce quantity from substance (as if).
Then you extrapolate the quantity '0'
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