Expert: Scott A Wilson - 11/2/2009

Question
Hello sir, one thing that always come to my mind and still its not being answered yet. To what extend truth in math? its about math philosophy. For example, 1+1 is 2..no one can deny it, is there any false in math?

Answer
With basic math, no.

In graduate math, there might be one,
though I can't recall studying sanything in graduate school.

A simple one is when squareroots are found.  There is always a choice as to whether to take the negative or positive,but most of the time the negative is not useful.  In physics, for example, if something was shot from some positive height and you were asked to see how long it was in the air, the negative answer would be how long it would have taken to get to the height it was shot from.

Another one is when nth roots are found.  Every number has n roots of this type.
For example, the squareroot of 16 is both 4 and -4.  The cube root of 8 is 2 if only reals are dealt with, but there are two more answer in the complex plain.  Converting the number from catesian (x,y) to polar (r,Θ).  The cube root of 8 would be the cube root of (8,0).  In polar coordiantes, this is also (8,0°), but here the zero is 0°.  The three cube roots are found by adding 360°•n, n=0,1,2 to the degrees and dividing each of them by 3.  Thus, the cube roots are (2,0°), (2,120°), and (2,240°).

A more complex example would be lim(f(x)) as x -> 0.
f(x) = 1 is x is fractional, 2 is x is real.
Here, there is no answer.

It seems like answers exist, but can't always be found.
Like √2.  Clearly it is a number, but it is not possible to find all of the digits.