A Comparison of Some Existence Tests
نویسندگان
چکیده
f(x) < 0, f(x) > 0. (1) Since f is continuous, the intermediate-value theorem guarantees the existence of some x∗ ∈ I satisfying f(x∗) = 0. The calculation of (1) can be verified by a computer. Hence, (1) describes an existence test for n = 1. We want to point out that the existence tests shall be performed by a computer; i.e., the test (1) shall be done by a computer. But as we will see in the following example, this is not always possible. EXAMPLE 2. Let y = f(x) = x− √ 2, x ∈ R.
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