Is it true that one equals zero, exploring paradoxes of mathematics Chapter 1
beside the genius contribution of special minds to the science, paradoxes and contradictions are recorded in the history of mathematics, either from a failed attempt to contribute to science, or simply from a Deliberately trick which aims to challenge minds.
In this article we introduce a simple paradox from the world of mathematics, in which we prove that one equals zero.
Beginning of the proof assuming variable x carries the value 1
In mathematical language: x = 1
it is clear that x2 = 1 also
Therefore: x = x2
if we minus the same value (1) from both Sides of the equation we get
x-1 = x2-1
using the rule of decomposition: x2-1 = (x-1) (x +1)
We get x-1 = (x-1) (x +1)
We divide both sides by (x-1)
and We get 1 = x +1
this is a simple equation with the solution x = 0 (by reduction of 1 from both sides)
we got that x=0 while the basic assumption was that x = 1
Conclusion 0 = 1
one equals zero ???!! is it true?
try to locate the mistake occurred.