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Irrational Numbers are contained by infinite numerical values?
Do you care? If we write out 1/7 we would require an infinite number of digits.meaning if we would to write a irrational number out , we need a infinite number of digits?
1/7 can also be written as 0.06666666..._{7}, and 1/3 can be written as 0.02222222..._{3}, requiring an infinite number of digits in these bases.Depends on the base of the number system used. 1/7 is 0.1_{7}, 1/3 is 0.1_{3}, both require infinite number of digits if they are to be written base 10.
I can write [itex]\sqrt{2}[/itex] with two symbols: 2 and [itex]\sqrt{\ }[/itex].meaning if we would to write a irrational number out , we need a infinite number of digits?
That's what I was thinking. We can write "2" without all the zeroes (2.000000...) because by convention we leave them off. What if by convention we left off .4142135623731...? Then things would be different (we'd write sqrt(2) as "1"). The point is, representations of numbers tell you about conventions, not so much about the numbers themselves.don't forget about the infinitely many zeros!