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The extension of this is the question of describing irrational numbers in terms of the exponent μ for which there are infinitely many approximations p/q satisfying | p/q − α | < 1/qμ.
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I want to echo Sarah Raybin in saying that the use of words like "schizophrenic" and "bipolar" in academia to describe irrational behavior perpetuates discrimination against people with psychiatric impairments in an ableist society.
Crazy, insane, ridiculous are all words to describe irrational behavior until they became words to describe awesomeness.
According to an independent report commissioned by the city manager, they described irrational and erratic behavior that scared them so badly, some laid out escape routes in case Dear were to "snap or go postal".
She often notes the balance between order and chaos in a work of art, as in the poems of Thom Gunn ("the poems seem lucid and orderly, but what they are describing is irrational"), or in Beckett's Happy Days: "The form is to remain strictly formal, yet the subject is to be chaos".
One senior Energy Information Administration official describes an "irrational exuberance" around shale gas.
Self-storage site managers describe an irrational tendency in some clients.
This finding further led Dr. Simonson and other scholars to describe widespread "irrational" behavior by consumers who made decisions not based on a product's actual value but on how the item was presented relative to other products.
Google executive chairman Eric Schmidt rejected the idea put forward by Labour leader Ed Miliband that the search giant should practise "responsible capitalism", arguing the company simply follows international tax laws – which he described as "irrational".
In two-hour judgement on the case on Thursday, Mr Justice Stuart-Smith concluded: "I am convinced that the decision taken by Mr Hardwick to suspend Mr Rhodes can only be described as irrational and perverse".
In the course of time, though, these original meanings had been lost (through, in Müller's notorious phrasing, a "disease of language"), so that the myths no longer told in a "rationally intelligible" way of phenomena in the natural world but instead appeared to describe the "irrational" activities of gods, heroes, nymphs, and others.
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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