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Definitions of irrational:

adjective: not consistent with or using reason
Example: "Irrational fears"

adjective: real but not expressible as the quotient of two integers
Example: "Irrational numbers"

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Alternative Terms
number natural-number real-number transcendental-number-2 ratio integer square-root mathematics almost-all commensurability-mathematics indian-mathematics shulba-sutras 800s-bc 500s-bc hippasus pythagorean-2 pentagram-2 pythagoras theodorus-of-cyrene nth-root eudoxus-of-cnidus euclid-s-elements negative-and-non-negative-numbers integral fraction abraham-de-moivre leonhard-euler complex-number euclid karl-weierstra kossak heine crelle-s-journal georg-cantor richard-dedekind salvatore-pincherle paul-tannery dedekind-cut leopold-kronecker continued-fraction joseph-louis-lagrange johann-heinrich-lambert adrien-marie-legendre bessel-clifford-function charles-hermite ferdinand-von-lindemann david-hilbert adolf-hurwitz paul-albert-gordan reductio-ad-absurdum irreducible-fraction coprime square-number pythagorean-theorem compass-and-straightedge-constructions golden-ratio logarithm algebraic-number polynomial intermediate-value-theorem divisor-2 field-mathematics long-division repeating-decimal pi algebraic-independence catalan-s-constant euler-mascheroni-constant uncountable-set countable-set metric-space-2 topological-space complete-metric-space g-delta-set proof-that-e-is-irrational eric-w-weisstein mathworld binomial-surd cubic-surd quadratic-surd-mathematics quartic-surd quintic-surd vitali-set generalized-power real-variable liouville-number natural-logarithm irrational surd

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