It is shown a triangle that has sides equal to 1 unit long, the diagonal of the triangle is equal to the square root of 2 is a contradiction in terms and means mathematics ends in meaninglessness
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"a triangle that has sides equal to 1 unit long, the diagonal of the triangle is equal to the square root of 2 is a contradiction in terms
The square root of 2. is equal to the length of the hypotenuse of a right triangle with lengths of length 1.
The square root of 2., often known as root 2, radical
Geometrically the square root of 2 is the LENGTH of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. Its numerical value, truncated to 65 decimal places, is:
1.41421356237309504880168872420969807856967187537694807317667973799…
Irrational numbers cannot be represented as terminating or repeating decimals.
Thus square root of 2 is a non finite number ie it never terminates –thus can never be constructed but the length of the hypotenuse is finite ie terminates
or
But by the mathematics the length of the hypotenuse is finite ie it terminates
Thus we have a contradiction the maths says
3) the hypotenuse is finite ie terminates ie can be constructed
but
4) the length of the hypotenuse is square root of 2 Ie is non-finite which does not terminate ie can never be constructed
Thus a contradiction in terms
Thus mathematics ends in meaninglessness
ALSO it must be impossible in our universe to construct a triangle that has sides equal to 1 unit long, with the diagonal of the triangle is equal to the square root of 2 .
As the diagonal can never be finite or constructed as its length is square root of 2 . which is non-finite and thus never terminates thus we can never construct a finite line joining the sides of the triangle as it length is square root of 2. which is non finite ie never terminates"