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Main Entry: 1ir·ra·tio·nal

Pronunciation: \i-?ra-sh(?-)n?l, ?i(r)-\

Function: adjective

Etymology: Middle English, from Latin irrationalis, from in- + rationalis rational

Date: 14th century

: not rational: as a (1) : not endowed with reason or understanding (2) : lacking usual or normal mental clarity or coherence b : not governed by or according to reason <irrational fears> c Greek & Latin prosody (1) of a syllable : having a quantity other than that required by the meter (2) of a foot : containing such a syllable d (1) : being an irrational number <an irrational root of an equation> (2) : having a numerical value that is an irrational number <a length that is irrational>

Are irrational deductions, such as the square root of 2 completely irrational in the sense that it is lacking normal coherence and are incomprehensible?

For example, no matter how many decimals we expand the square root of 2, when we multiply itself it is always 1.9999 ... (with some random numbers at the end depending on the exact expansion)

So how could the square root of 2 be comprehended, how can it exist logically and conceptually in the mind except on a superficial level that it is the number that when multiplies by itself equals two?

Are not irrational numbers irrational in the fullest sense of the word? There is no number, or integer that when multiplied by itself that will equal two, stating an infinite expansion will not suffice because that seems illogical, yes? An infinite expansion is not possible .

Thank you,