Does this equation (x² = 2) have a solution for x? If not, why not?
If you propose that x is a number that has a decimal expansion that do not terminate, then that is not a specific number, right? And then it is no solution?
-
Recent Comments
mariusmyburg on “Male and Female… toni on “Male and Female… Dawie on Religulous – a ‘re… yetsta on Visual Studio 2010 Beta yetsta on Sometimes, I envy creatio…
Stoffel said
I’m an ignoramus concerning mathematics, but you may be interested to know that the square root of 2 is part of the international standard (ISO) formula for paper sizes (A0, A1, A2, A3, A4 etc). The formula is that the ratio between the two sides of any sheet of paper = 1:1,4142… Example: the short side of the popular A4 sheet of paper = 210 mm, the long side = 210 x 1.4142… = 297 mm. Any idea who devised this “irrational” formula?
mariusmyburg said
That is fascinating! It was a real surprise to learn that the ratio between the height and the width of paper is the square root of two!
http://simple.wikipedia.org/wiki/Paper_size
TheVAL said
Yes, that is really amazing about those paper sizes, I haven’t ever even think of that!
mariusmyburg said
So just to point out, the ‘rationalization’ behind this fact seems to be that, as you go from A0 to A1 to A2 etc, you halve the page; and halving a page that has as a height-to-width ratio of the square root of two, will keep that same ratio. In effect, you are scaling the who page uniformly by halving it. Fascinating! Thanks for pointing out this ratio Stoffel.