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## Main Question or Discussion Point

Consider two functions f, g that take on values at t=0, t=1, t=2.

Then the total error between them is:

total error = mod(f(0)-g(0)) + mod(f(1)-g(1)) + mod(f(2)-g(2))

where mod is short for module.

This seems reasonable enough.

Now, consider the two functions to be continuous on [0,2].

What is the total error now?

My guess is that it is the integral of the absolute value of their difference divided by the length of the interval:

total error =1/2 * integral from 0 to 2 of mod(f(x)-g(x)) dx

Is this right?

Or is the error evaluation done in a different way?

Then the total error between them is:

total error = mod(f(0)-g(0)) + mod(f(1)-g(1)) + mod(f(2)-g(2))

where mod is short for module.

This seems reasonable enough.

Now, consider the two functions to be continuous on [0,2].

What is the total error now?

My guess is that it is the integral of the absolute value of their difference divided by the length of the interval:

total error =1/2 * integral from 0 to 2 of mod(f(x)-g(x)) dx

Is this right?

Or is the error evaluation done in a different way?