Question on Dedekind Cuts

v8archie

Math Team
Dec 2013
7,712
2,682
Colombia
A carpenter doesn't deal in decimals. His ruler (a tape) is divided in 1/32's. He works to 1/32's or maybe 1/16's.
A cabinet maker would work to 1/64th's. His ruler is probably a yard stick graduated to 1/64th's.
A machinist deals in thousandths. His ruler is a micrometer or vernier caliper which reads to three (.001) or four (.0001) decimal places.
There is constant conversion in practice: 1/16 = .0625 for example

To convert Pi to a decimal representation: Take a circle of diameter 1. Then unwind the circle onto a line with same unit 1. The decimal representation of the point where the line ends can be found as in:

http://mymathforum.com/real-analysis/345652-decimals-continuum.html
Yeah, I think everyone knows that craftsmen and engineers use approximations that suit the tolerances they work too. It has nothing whatever to do with the construction of the real numbers.
 

skipjack

Forum Staff
Dec 2006
21,478
2,470
. . . by standard (High School) division.
Using division isn't an explanation of how to put a period after a natural number and then read it in reverse to get the decimal for 1/9. Is that your best effort?
 
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