What is difference in approaches between using standard part in NSA and limit? I don't mean technique of differentiation or integration.
Can somebody explain it on example?
Thanks.
2026-03-25 23:08:35.1774480115
What is difference in approaches between using standard part in NSA and limit?
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In NSA, the concept of limit is defined in terms of the standard part. Thus, to calculate the limit of $f(x)$ as $x$ tends to $0$, one would perform two steps: (1) evaluate $f$ at an infinitesimal value $x=\alpha$, and (2) take the standard part. The limit exists if and only if the standard part exists for all infinitesimal $\alpha$, and furthermore they all have the same value.