You are both correct. The transition from the first and second step is often the hardest to make (though the the transition from the second and third step should not be overlooked as it can have its own problems as well). When you first learn mathematics, the focus is on applications: Compute this, find this, and calculate that. You dive into computation without the theory behind it. Transitioning from phrases such as “compute” and “find” to “verify” and “prove” is naturally difficult because the emphasis on computation is lost. Mathematics has to be relearned from the perspective of verifications and proofs. To be a mathematician, however, one must be affluent with all the questions–“compute”, “verify”, or otherwise. A mathematician must apply rigour where necessary and computation where necessary.

I am glad you have taken the time to explore more of calculus, Eric. Though a relatively young mathematical sub-discipline, its implications are fundamental to our understanding of the universe. We actually are going to use calculus for the grand finale blog. If you have time, check out infinite series.

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