110411-1600 edt
In my first calculus book "Elements of The Differential and Integral Calculus", by Granville, Smith, and Longley, 1934, the delta symbol is introduced in Chapter III with the definition:
delta y denotes an increment of y
This does not imply infinitesimal.
However, if you take a fraction such as delta y/ delta x and evaluate this as delta x approaches 0, and further add the condition of the limit as delta x approaches 0, then this becomes the definition of the derivative of y over x. This is written as
dy/dx = the limit as delta x approaches 0 of delta y / delta x
Shown more accurately on page 21 of the above book.
So delta means a difference and not necessarily small. But if you then study how a function varies as the independent variable approaches 0, then you have obtained the derivative of that function. And yes in this class of math you can divide by zero and get a finite value. But you divided by zero by determining what happens as you make the increment in the independent variable smaller and smaller.
As was mentioned above if you have the equation r = e/i and apply this to a constant value resistor independent of the value of i you will find that for any small change in i that you get a directly proportional small change in voltage.
If you consider a diode and perform an experiment where there are small changes in current at different current levels the result will be different ratios of voltage change to current change as the current is changed. This is a non-linear resistor.
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