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Real numbers cannot have ordinal values.

Real numbers can't have ordinals because it's impossible to tell what the successor to a real number is. What is the successor to 2.3? Is it 2.31? Or is it 2.301? Or does 2.3001 sound more convincing? The answer is there is no ordinal relationship here. There is no successor to a real number. Infact between any two real numbers there exists an infinite amount of other real numbers.

Madhu Nayakkankuppam
Thu Jan 21 17:49:55 EST 1999