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Can I write the integer 2 with some zero before as : 002

Can I precede all integer by an infinity of zero : ..........002

Does it make sense to write an integer as an infinity of numerals ? For instance, is the infinite sequence of 1 (....................11111111111111111111111111111111111111) an integer?

For all these questions, can you give me references (book, article) at undergraduate level (better) or graduate level?

Thanks

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    Of course you can introduce that unusal definition, the question is "does it make sense". You can't simply say you "precede all integers by an infinity of zeroes", the concept of infinity is rather a limit than something you can work with, please use the search too to look for questions about infinity.2012-01-24
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    The decimal expansion of a number makes sense. For instance 0.99999999.... is equal to 1. I'm asking myself if this kind of notation is also used, not for the decimal part but "on the left" for the integer part. In the notation 0.999....., I suppose we employ a countably infinite set. I'm wrong with that?2012-01-24
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    @Mathieu, you have discovered the p-adics, which is far from wrong, although they are uncountable just like the reals.2012-01-24
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    Thanks, I will read about it.2012-01-24

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