Never thought I'd see calculus references here...
I thought calculus was a robot in the cartoon "Futurama"?
oh wait that was calculon...sorry
This thread has gone clear over my noggin!
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Never thought I'd see calculus references here...
Part of your problem
I think it's something like this.
0.9999... Isn't one, if it was one, it would be 1.
It is however a very close approximation of one.
It is not one simply because there is ALWAYS a remainder.
Add 0.0001 to 0.9999 and you get 1 just as if it were to any decimal point or infinity.
Factually, accurately 0.9999... Will never and can never be one it can only be approximated to be one. Imo.
It's really counter intuitive. Before having university classes on that matter, I didn't believe it either. But yeah, I still think that the best way to explain it (without it getting complicated) is this one:
1 = 1
(3/3) = 1
(1/3) + (1/3) + (1/3) = 1
0.3333... + 0.333... + 0.33333... = 1
0.9999... = 1
There's no approximation anywhere in there.
WOW . . I just discovered that .00001=.99999!
Amazing. Time to hit the college prep math books for a refresher.
Next thing you know, Three Dog Night will be sued for telling us that 'One is the Loneliest Integer' when the Internet will prove with unfailing logic that 4 is actually the loneliest integer.
So 1 is exactly equal to .9999? And .9999 is exactly the same as 1? What about .9? What is that equal to?
If I borrow a dollar from you and you really need to be paid back in full, can I settle the debt with 99 cents? Same as a dollar, right? If I brrow three or five or a grand, can I settle the debt in full by paying you just little less than I borrowed? Apparently I can. Will you be my next loan officer?
So, .9999 = 3/3 and 1/3+1/3+1/3=.9999?
And so forth?
Your mistake is in the 4th line: 0.3333... + 0.333... + 0.33333 = .9999 not one which is equal to .999994 x the Internet = Bollocks. Some of us seem to leave up the missing piece of the math. I'll call it B for Bollocks.
Therefore, .9999 (B) = 1
I do know that E-MC Squared is not true. E=MC Hammer and You Can't Touch That, my friend.
remember that 0.99999... repeating is NOT the same number as 0.9 or 0.99 or 0.999 or 0.9999999999999999999999999
The way I was taught mathematics and composition, an overline placed above the sequence is used to indicate a repeating sequence, and the ellipsis is used in composition (writing) to indicate that text has been skipped. An ellipsis can be used in mathematical notation for the same purpose as with composition, but isn't interchangeable with the overline. But because many websites and other Internet services don't offer the entire range of possible characters, substitutes for full mathematical notation are often used for convenience.That is one way to show repeating decimals, but the ellipses "..." is also widely accepted in mathematics to signify a repeating sequence.
The way I was taught mathematics and composition, an overline placed above the sequence is used to indicate a repeating sequence, and the ellipsis is used in composition (writing) to indicate that text has been skipped. An ellipsis can be used in mathematical notation for the same purpose as with composition, but isn't interchangeable with the overline. But because many websites and other Internet services don't offer the entire range of possible characters, substitutes for full mathematical notation are often used for convenience.
When it comes to decimal numbers like a string of nines to the right of the decimal, you can either round up to a solid 1 or accept that adding more nines will approach but never reach 1.
.99999... does in fact equal 1 and can be easily mathematically proved.
Let x=.9999999......
Therefore 10x=9.99999.......
10x-x =9x. == 9.99999.....-.999999....=9
So 9x=9
9x
don't let students know that (some profs say that 69.999 doesn't equal 70, lol)
Never thought I'd see calculus references here...
It depends on the setting really. If your manufacturing gears with a wire edm then .9999 is still .0001 underside from 1.00000. now if you have a geometric tolerance of lets say +- .00001 than that dimention being at .9999 would bring you out of tolerance by .00009 rendering the part non conforming and scrap.
Don't forget that the ellipses ("...") at the end of ".999..." are very important / significant.
don't let students know that (some profs say that 69.999 doesn't equal 70, lol)
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