I always took this to be 'there is only one success, there are many failures', there is only one zero, but many values other than zero. It seemed kind of logical.
> zero has many properties that other numbers do not
In particular, zero is the additive identity [0] in almost all the "usual" number systems in which it appears. That is roughly speaking, it is the only A such that X + A = X, for all X, where X and A are elements of the number system (e.g. field of real/complex numbers).
The integers form a group under multiplication though and a key property of a group is that every element has an inverse. So how does the definition hold if there is nothing that could be considered an inverse for the number 0? Curious about this... I never thought about it before.
That's idiomatic, not an inherent property of the numbers themselves. You're basically arguing that because we do it in one context we do it in another context, but it doesn't answer the question of why.
Well, an interesting fact is that every nonzero rational number has two equal representations in some bases, e.g. 0.999...=1. Zero is then is the only rational number with just one representation.
Well, the convention in maths is that we never add trailing zeros, since they wouldn't as any information. Unlike in other sciences, where they represent measurement precision.
