the 18th century, Euler and other mathematicians relied on a broad interpretation of the law of continuity or, as Cauchy will call it, the *generality of algebra*. This involved manipulation of infinite series as if they were finite sums, and in some cases it also involved ignoring the fact that the series diverges. The first serious challenge to this principle emerged from the study of Fourier series when new types of functions arose through the summation thereof. Specifically, Cauchy rejected the principle of the *generality of algebra*, and held that a series is only meaningful in its radius of convergence. Cauchy’s approach was revolutionary at the time and immediately attracted followers like Abel. Cauchy in 1821 was perhaps the first to challenge such a broad interpretation of the law of continuity, with a possible exception of Bolzano, whose work dates from only a few years earlier and did not become widely known until nearly half a century later. For additional details on Cauchy see [@KK11], [@KK12], [@BK], [@Ba14]. For Euler see [@KKKS] and [@Ba16b].

Non-examples: EVT and IVT
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It may be useful to illustrate the scope of the relevant results by including a negative example. Concerning results such as 