Irrational Numbers
Definition
Definition
Irrational numbers are numbers that cannot be expressed as a fraction of 2 integers. This is represented by the symbols ℝ \ ℚ which means the set of all real numbers excluding all rational numbers.
Irrational numbers are numbers that cannot be expressed as a fraction of 2 integers. This is represented by the symbols ℝ \ ℚ which means the set of all real numbers excluding all rational numbers.
Historically, these numbers were referred to as ἄλογος (alogos) by the Early Greeks (Eg. Euclid) found the idea of such a number to be quite illogical.
Historically, these numbers were referred to as ἄλογος (alogos) by the Early Greeks (Eg. Euclid) found the idea of such a number to be quite illogical.
Famous Examples of Irrational Numbers
Famous Examples of Irrational Numbers
√ 2, The Square Root of 2 was proven to be irrational by the Early Greeks (possibly Hippasus of Metapontum, a student of Pythagoras). In one story, he was thrown off the boat and drowned to death by his fellow classmates for his forbidden discovery.
√ 2, The Square Root of 2 was proven to be irrational by the Early Greeks (possibly Hippasus of Metapontum, a student of Pythagoras). In one story, he was thrown off the boat and drowned to death by his fellow classmates for his forbidden discovery.
π, Pi was proven to be irrational by Lambert in the 1760s.
π, Pi was proven to be irrational by Lambert in the 1760s.