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→What is the problem? Aren't rational numbers good enough?: Spelling/Grammar Check, typos fixed: less then → less than
::''The rational numbers do not satisfy the least upper bound property.''
::''The rational numbers do not satisfy the least upper bound property.''
For example, if we can only use rational numbers, the set of numbers that have squares less then 2 has no rational least upper bound. 1.4142136 is an upper bound, but 1.41421357 is a smaller one. The exact square root of 2 is the least upper bound that we need, but it isn't rational.
For example, if we can only use rational numbers, the set of numbers that have squares less than 2 has no rational least upper bound. 1.4142136 is an upper bound, but 1.41421357 is a smaller one. The exact square root of 2 is the least upper bound that we need, but it isn't rational.
==Two ways to define the reals formally==
==Two ways to define the reals formally==