hmmm.. i'm not a very mathy person but seems like an interesting question.

Aren't they both just infinite? There's no such thing as a bigger inifinite?

thinking about it out loud here tho I would say that every natural number is a BIGGER number than every real number between 0-1 because, well, 2 is bigger than 0-1.

but then again since you said corresponding to every number.... 0.000000to infiniitiy -1 is a number in itself, so, you have infinite numbers, along an infinite number of 'places'.

Final Answer, you save lives by natural numbers, because real numbers have an infinite number of 'digits' per 'places' & those 'Places' are equal to all natural numbers.