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According to the formal definition of a leading zero, is the zero itself considered a leading zero?

Ahmed Hussein
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This question has more of an opinion based answer. However, let us call any number with leading digit $0$ as 'good'. We can easily see that any non-zero integer can be written in a 'good' way by just adding a zero before the leading digit. Thus, when any non-zero integer can be written in a 'good' way, it would make sense to say that zero itself can be written in a good way. A 'good' number moreover needs a minimum of one zero, so it would be logical to say that $0$ is good.

Besides, in A000030 of the OEIS sequence, we can see that the leading digit of zero is $0$. This shows that $0$ is a good number.

Now, our answer depends upon how you define a leading zero. If a leading zero is just zero as the leading digit, then our answer is yes. However, if we go with the Wikipedia definition, the answer is no, as we can see that we must have our zero, before any non-zero digit. Thus, this would require a non-zero digit to be present.

However, definitions from the internet need not be correct. Depending on what definition you go with, your answer might vary.

Haran
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  • I got your point, but I am expecting an official formal definition that states the fact without opinions: "Is the answer yes or no and why" – Ahmed Hussein Dec 31 '18 at 07:38
  • What definition do you go with? Do you agree with the Wikipedia definition? Once you put forth the definition that you think is correct, the question can be answered. – Haran Dec 31 '18 at 07:42
  • I will agree if it is the official mathematical definition. – Ahmed Hussein Dec 31 '18 at 07:43
  • @AhmedHussein there is no such thing as an official mathematical definition. There are many opposing views on even basic definition-related concepts. All that one can say is that if you agree with the definition that you have posted, then the answer is no – Haran Dec 31 '18 at 07:45
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    For example, there is conflict on whether zero is an even number or not. Even numbers are such basic concepts in math. Yet, some people argue that zero is even, as $\frac{0}{2} = 0$ and others argue that it is neither even nor odd. However, I have my own opinion that it is even, since it seems natural to extend the domain of divisibility from the naturals to integers (and even more!), and zero provides a starting point for divisibility. When people work with Number Theory, if you prove that a number has infinitely many distinct factors, it is zero! You must decide the definition you go with. – Haran Dec 31 '18 at 07:51
  • @Haran There is no "conflict" among mathematicians over whether zero is even, though the matter does confuse some non-mathematicians. Cf. https://math.stackexchange.com/questions/15556/is-zero-odd-or-even . I think a better example is whether or not zero is a natural number. – Eric M. Schmidt Dec 31 '18 at 08:11
  • @EricM.Schmidt Yes you are right. That is a better example. I think it would make the point. Anyways, the matter is that definitions are flexible. – Haran Dec 31 '18 at 08:18