# Why does this spatial discretization with n intervals have a position of (n-1)/n for each interval?

Hello, all.

I am learning about how to descritize the Heat Equation in space. This case involves a rod along the xi-axis with some thermal conductivity, kappa.

Now, I understand that one would descritize it so that they can utilize a set of points to sample and approximate the behavior of a system as a whole.

According to the following picture, you can descritize the rode into a finite number of elements, with the quantity of these being n. I believe that I understand why each interval has a length of 1/n. My brain is connecting to the the frequency and period of a wave, where f = 1/T. Let's say that I want to have 100 samples, then the spatial distance between each equidistant sample must be 1/100 so that x goes from [0,1].

However, I do not understand why the spatial variable can be represented as (n-1) / n, as in the following equation. Can someone explain why? Also, I notice that the equation at the bottom changes an "n" to an "i". Could this be a typo?

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