Prove 3/3 ≠ 1: Math Puzzle Challenge

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The discussion centers on the mathematical assertion that 3/3 equals 1, while exploring the concept that 0.999... is equal to 1. Participants argue that 0.999... represents an infinite series that converges to 1, thus reinforcing the idea that different decimal representations can denote the same value. Some contributors express disbelief in this equivalence, suggesting it contradicts their understanding of numbers. Ultimately, the conversation highlights the complexities of decimal notation and the nature of infinite series in mathematics.
  • #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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