Can I add any number of zeros to 0.00 ... 1?

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SUMMARY

The discussion centers on the concept of adding zeros to the decimal representation of numbers, specifically examining the implications of inserting zeros in the sequence of 0.001. Participants conclude that while one can add a finite number of zeros before a non-zero digit, an infinite sequence of zeros followed by a non-zero digit leads to an undefined representation. The distinction between "arbitrary" and "infinite" is emphasized, clarifying that while one can add any finite number of zeros, an infinite number of zeros results in a number that cannot be properly defined within the positional decimal system.

PREREQUISITES
  • Understanding of positional numeral systems
  • Familiarity with decimal representation and real numbers
  • Basic knowledge of limits and sequences in mathematics
  • Concept of infinitesimals and their relevance in analysis
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  • Study the concept of Cauchy sequences in real analysis
  • Investigate the differences between finite and infinite sets in mathematics
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  • #31
Sadly, our post limit has exceeded the number of zeros you want to add, and there have been sufficient attempts to answer this question. Therefore, it's time to close this thread and thank all who contributed.

The OP might be interested to read about hyperreal numbers:

https://en.wikipedia.org/wiki/Hyperreal_number

and their connection to Calculus but that's for another time and another thread.

Jedi
 
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Likes nmz, SammyS and PeroK

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