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Does there exist to be any real number r such that what the title above says will become true ?
Thank you
Thank you
I know definition of real numbers but the fact is that I am studying about sequence, series, with inf and sup and these problems appear in the exercise pages which I am required to finish before next week's Tuesday. This means I have got to prove this theory in relation to sup and inf...matt grime said:Erm, the *definition* of the real numbers assures you that there is such a number, and that it is unique up to sign. That is the proof, you do know *a* definition of the real numbers?
Proving Z has no inf or sup should be very easy: how do you think you do it?
matt grime said:sup means the least upper bound, inf means greatest lower bound.
I am glad defiinitions are straighten out. If it had been lub and glb, not sup and inf, I might have guessed as much.
"Real number R^2=8" is a mathematical expression that represents a pair of real numbers (x,y) in a two-dimensional space, where x and y are both equal to 8.
R^2=8 represents a pair of real numbers (x,y) where both x and y are equal to 8. R^2=16 represents a pair of real numbers (x,y) where both x and y are equal to 16. The only difference between the two is the value of the numbers.
To graph R^2=8, you can plot a single point on a two-dimensional coordinate plane at the coordinates (8,8).
The "2" in R^2=8 represents the dimension of the coordinate plane. In this case, it is a two-dimensional or 2D space. This means that the pair of real numbers (x,y) exists on a plane with two axes, the x-axis and the y-axis.
R^2=8 is not directly related to the concept of area. However, in a two-dimensional coordinate plane, the value of R^2 represents the area of a square with side lengths of 8 units. So, in this case, R^2=8 can be interpreted as the area of a square with side lengths of 8 units.