Is 0.9999... Equal to 1? Debunking the Myth and Understanding the Concept

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SUMMARY

The discussion centers on the mathematical equivalence of 0.9999... and 1, asserting that they are indeed equal. This concept is supported by various mathematical proofs, including the use of limits and infinite series. Participants emphasize the importance of understanding the notation and implications of repeating decimals. The conversation highlights the common misconceptions surrounding this topic and encourages deeper exploration into the nature of numbers.

PREREQUISITES
  • Understanding of infinite series and limits in calculus
  • Familiarity with decimal notation and its implications
  • Basic knowledge of mathematical proofs and logic
  • Concept of real numbers and their properties
NEXT STEPS
  • Research the proof that 0.9999... equals 1 using limits
  • Explore the concept of repeating decimals in real analysis
  • Learn about the properties of real numbers and their implications
  • Investigate common misconceptions in mathematics and their resolutions
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Mathematics students, educators, and anyone interested in understanding the nuances of decimal representation and mathematical proofs.

Raza
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At first, when I saw this, I was deeply shocked and lost the believe that math is absolute. Like the thinking that if Math can prove it, it must exist and if it can't, it doesn't exist.

So is 0.99999...=1 illogical?

also, is it fair to say that 1.00=1?

Sorry if this question is already posted or it's in the wrong forum.
 
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0.99999(9) is 1
It's right and logical. Unfortunately, I don't remember the prove now, it was on the first grade in University.
 
This has been slogged out many times: there's no need for another discussion thread.
 
The real question, Raza, is do you know what 0.9999... means? If not, you certainly can't say that 0.9999...= 1 is an error! If you believe you do, what do you think 0.9999... means? The fact that you ask if 1.00= 1 makes me wonder.
 

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