At the very last step, highlighted in red, it states that if this, then that sort of, and I'm not sure how those comparisons explain the issue of proving Pascal's Triangle increasing until the middle, then decreases.
Is it saying (for the first one) that if the value of one entry is less than the next, then the entry comes before the next one, and vice-versa for greater than? If this is the case, how does that make sense for equals? If the value of one entry is greater than the next, the two occur in the same spot? How can two occur in the same spot? (I know in odd rows the middle is duplicated, but they're still difference positions within the row.)
Could anyone offer an explanation?