The Swiss mathematician Euler erred gravely in reaching his conclusion that 0.999… = 1. Euler failed to realize that by definition, 0.999… must be less than 1. So why did he fail in this regard?

The answer becomes evident when one realizes that Euler was among the first mathematicians to start treating all mathematical objects as numbers without paying detailed attention to the attributes and definitions of the same.

Euler incorrectly assumed that the ill-defined quasi-number concept of 0.999.. is a number, and applied some of the number theorems he already knew, to reach (erroneous) conclusions regarding its equivalence to 1.

He was famous for being a proponent of quasi-number objects, for example, the complex “numbers”. Euler is associated with many ill-defined concepts that include complex numbers. One well-known ill-formed identity is the equality relating pi, sqrt(-1), -1 and e. In truth, none of these concepts except -1, are well-defined.

Since Euler, many modern mathematicians have succumbed to these erroneous and toxic ideas.

Perhaps I should not be too critical of Euler because his introduction of function notation was a great contribution to mathematics.