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I_am_learning
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It appears the maximum value of x = 0.999... . But 0.999... = 1. But max value of x cannot be 1 based on the criteria. What is the maximum value of x then? It's puzzling me.
I_am_learning said:Is it that it does not have maximum or is it that we cannot numerically represent it?
If we are asked to compare "the maximum value" and 1, we still say 1 is the larger number, won't we?
Thanks for the feedback.
micromass said:There is no maximum value. That is, there is no real number ##a## such that ##a<1## and such that ##b\leq a## for all ##b<1##.
I_am_learning said:Thank you micromass.
I now get that there isn't any number which you can claim to be the maximum, because whatever number (<1) you claim, I always got another number (<1) but greater than yours. Since there isn't any number, the comparison cannot be done. But I have this gut feeling that even if we can't have any number as 'the maximum', we can still compare and say, 'the maximum' is less than 1.
If there is no maximum for such open intervals, is someone 'correct' to ask this question? If yes what is your answer?
Provided |x - 3| < 5
Quantity A: Least value of x
Quantity B: -2
Compare Quanity A and B and mention which of them is greater or if they are equal or if the relation cannot be determined.
P.S.: You mentioned 'real'. Is there a complex solution?
The maximum value of x would be 1, as it is the closest number to 1 that is still less than 1.
Yes, there can be a numerical value for x if it is less than 1. It can be any decimal number between 0 and 1, but the maximum value would still be 1.
No, if x is less than 1, it cannot be equal to 1. It can only approach 1 as a limit, but it will never reach 1.
If the inequality changes to x<2, the maximum value of x would change to 2. This is because 2 is the closest number to 2 that is still less than 2.
Yes, x can be a negative value if it is less than 1. It can be any negative decimal number between 0 and 1, but the maximum value would still be 1.