Prove 3/3 ≠ 1: Math Puzzle Challenge

  • Context: High School 
  • Thread starter Thread starter krypto
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Discussion Overview

The discussion revolves around the mathematical assertion that 3/3 is equal to 1, with participants exploring the implications of decimal representations, particularly the recurring decimal 0.999... and its relationship to 1. The scope includes mathematical reasoning, conceptual clarification, and debate over the nature of infinite series and convergence.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • Some participants assert that 3/3 equals 1, but argue that 0.999... is an alternative representation of 1, leading to the conclusion that 3/3 does not equal 1.
  • Others counter that 0.999... is indeed equal to 1, citing mathematical principles and the concept of Cauchy sequences.
  • One participant emphasizes that an infinite series converges to its limit, suggesting that 0.999... equals 1 due to the nature of convergence in mathematics.
  • There are claims that the terms "convergence" and "member" apply to sequences and not to numbers themselves, indicating a distinction in how numbers are defined.
  • Some participants express skepticism about the equality of 0.999... and 1, suggesting that proofs supporting this claim contain contradictions.
  • Discussions include the idea that different decimal representations can lead to confusion, with references to how numbers are constructed and defined in mathematics.

Areas of Agreement / Disagreement

Participants generally disagree on the equality of 0.999... and 1, with multiple competing views presented. Some assert the equality while others reject it, leading to an unresolved debate.

Contextual Notes

Limitations include varying interpretations of mathematical definitions, the nature of infinite series, and the implications of decimal representations. The discussion reflects differing levels of understanding and acceptance of mathematical concepts.

  • #31
So, if I chose another symbol for 1, its numerical value would change?
 
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  • #32
nope cos it still means 1 even if u named it bob
 
  • #33
Precisely. So writing 0.999... shouldn't falsify 0.999... = 1, right?
 
  • #34
A recurring decimal can be written like:

S = A*r^n

0.999... = 0.9*0.1^n

Sum to infinity of a converging series: \frac {A}{1-r}

So, \frac {0.9}{1-0.1}=\frac {0.9}{0.9} = 1
 
  • #35
It's times like this that we need to consider switching to a duodecimal system. In duodecimal 1/3 = 0.4

Much easier.

\sigma

The Rev
 
  • #36
Well, since nobody seems to be learning anything, I'll close it up.
 

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