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The Egyptian example is even more pertinent.
In recent work, John Manchak (2009) has argued that this example is even stronger than it appears, as underdetermination persists even if we permit ourselves the assumption that all physical laws we determine locally apply throughout the universe as a whole.
To deal with the case x = n > 0, merely take a neighborhood of x with radius less than min { k β n / ( β n + 1 − β n ), k β n + 1 / ( β n + 2 − β n + 1 ) }. Notice that the mapping of the above example is even locally contractive in the sense of Rakotch [6], but it is fixed-point-free.
Lest you jump to conclusions or get your hopes up unrealistically high, this example is, even in our very selective study, the exception, rather than the rule.
An example is even though the Sugarhill Gang has one of the most memorable rap songs of all time, the first album by the group was composed of rapping and singing.
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Courts are still untangling the disturbing allegations — were girls as young as 12 forced to marry middle-aged men? — but the questions that cut deepest, about society's laws versus religious freedom, for example, are even harder to answer.
The woman with the blocked artery, for example, was even prompted to indicate if the service saved her life — a smart touch that not only helps the site track its success, but offers incredibly powerful reason for a doctors to keep coming back and answer more questions.
Also, notice that some mappings in this example are even discontinuous at their unique common fixed point 2. By choosing A, B, S, and T suitably, we can drive a multitude of common fixed-point theorems for a pair or triod of self-mappings.
Few models of genetic hitchhiking in subdivided populations have been developed and the rarity of empirical examples is even more striking.
They are usually under 4% alcohol, and some examples are even lower alcohol than that.
In war-torn Aceh and Maluku, for example, there is even a shortage of judges to staff the courts.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com