Given 11 different natural numbers, none greater than 20. Prove that two of these can be chosen, one of which divides the other.
2 answers:
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For the integer values of the interval <span>-2 ≤ x ≤ 2, that is for {-2, -1, 0, 1, 2}, the function works as follows:
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[-2]=-2, [-1]=-1 [0]=0 [1]=1 [2]=2,
as each of -2, -1, 0, 1, 2 is smaller or equal to themselves.
Each value in between, produces the integer to their right.
For example, [1,25]=2, because 2 is the smallest integer, greater than 1,25.
Thus, the output of each non-integer value is the closest integer to the right. Some more examples:
[0,7]=1, [0.46]=1, [-0,5]=0, [-1,33]=-1.
The graph is as shown in the picture.
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[-2]=-2, [-1]=-1 [0]=0 [1]=1 [2]=2,
as each of -2, -1, 0, 1, 2 is smaller or equal to themselves.
Each value in between, produces the integer to their right.
For example, [1,25]=2, because 2 is the smallest integer, greater than 1,25.
Thus, the output of each non-integer value is the closest integer to the right. Some more examples:
[0,7]=1, [0.46]=1, [-0,5]=0, [-1,33]=-1.
The graph is as shown in the picture.