The difference between Irrational and Transcendental

When used as nouns, irrational means a real number that can not be expressed as the quotient of two integers, an irrational number, whereas transcendental means a transcendentalist.

When used as adjectives, irrational means not rational, whereas transcendental means concerned with the a priori or intuitive basis of knowledge, independent of experience.


check bellow for the other definitions of Irrational and Transcendental

  1. Irrational as an adjective:

    Not rational; unfounded or nonsensical.

    Examples:

    "an irrational decision"

  2. Irrational as an adjective (mathematics, arithmetic, number theory, not comparable):

    Of a real number, that cannot be written as the ratio of two integers.

    Examples:

    "The number π is irrational."

  1. Irrational as a noun:

    A real number that can not be expressed as the quotient of two integers, an irrational number.

  1. Transcendental as a noun (obsolete):

    A transcendentalist.

  2. Transcendental as a noun (philosophy, metaphysics, Platonism, Christian theology, usually plural):

    Any one of the three transcendental properties of being: truth, beauty or goodness, which respectively are the ideals of science, art and religion and the principal subjects of the study of logic, aesthetics and ethics.

  1. Transcendental as an adjective (philosophy):

    Concerned with the a priori or intuitive basis of knowledge, independent of experience.

  2. Transcendental as an adjective:

    Superior; surpassing all others; extraordinary; transcendent.

  3. Transcendental as an adjective:

    Mystical or supernatural.

  4. Transcendental as an adjective (algebra, number theory, field theory, of a [[number]] or an [[element]] of an [[extension field]]):

    Not algebraic (i.e., not the root of any polynomial that has positive degree and rational coefficients).

  5. Transcendental as an adjective (algebra, field theory, of an [[extension field]]):

    That contains elements that are not algebraic.