Profpointy
Legendary Member
No, they are the same. .33 recurring is exactly 1/3. Thus 3 * one of them can't be different from 3* the other
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No, they are the same. .33 recurring is exactly 1/3. Thus 3 * one of them can't be different from 3* the other
Profpointy
Legendary Member
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No, they are simply different ways of representing the same thing, rather than different things almost but not quite equal
No, they are simply different ways of representing the same thing, rather than different things almost but not quite equal
Electric_Andy
Heavy Metal Fan
- Location
- Plymouth
I would have thought that 0.9 recurring is infinitely close to 1 but not equal to it? Surely the only thing equal to 1 is 1
OP
OP
Deleted member 26715
Guest
I concur
Electric_Andy
Heavy Metal Fan
- Location
- Plymouth
That doesn't seem rational. It might be taught that way for maths or physics, but if anything is 0. something of 1, it's an infinite fraction, meaning that no matter how long the recurring 9's go on for, it'll never reach 1. A bit like if you keep halving the distance between 2 points, they'll never touch. If you had a microscope strong enough (infinitely strong if you will) you can always keep measuring the distance and just keep adding fractions of 1 on to the end.
Ok assume that 0.9999... is less than 1. If you add something (> 0) to any of the digits, the result is > 1, so it must be the closest number to 1, but different.
Then
1 - 0.99999..... = a > 0 (say)
And
0.9999... < 0.9999... + a/2 < 1
But that can't be as 0.9999... is the closest number to 1. So 0.999... is not less than 1.
Any decimal which can be written down (finite) has this property so
3.6 = 3.59999999.....
Etc
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Profpointy
Legendary Member
Here's a (non-proof) way of looking at it.
1 .33 recurring is exactly 1/3
We do agree on that I assume.
2 Multiply 1/3 by 3 - what do we get ?
3 Multiple .33 recurring - do we somehow get a different answer?
1 .33 recurring is exactly 1/3
We do agree on that I assume.
2 Multiply 1/3 by 3 - what do we get ?
3 Multiple .33 recurring - do we somehow get a different answer?
DaveReading
Don't suffer fools gladly (must try harder!)
- Location
- Reading, obvs
Recurring decimals aren't a problem, because they're not on the syllabus.
It's things like understanding that, for example, 12.5 isn't the same as 12.05, that I meant when I referred to place value after the decimal point.
Recurring decimals aren't a problem, because they're not on the syllabus.
It's things like understanding that, for example, 12.5 isn't the same as 12.05, that I meant when I referred to place value after the decimal point.
Sorry got carried away :-).
matticus
Guru
That makes sense to me.
Another angle is that "infinity" rarely "makes sense" as a concept - you have to define what you actually mean by it!
e..g what IS 0.3...... ?
Well it's actually a third, isn't it? It's the amount you get if you divide something up into 3 bits. That's the only thing that matters - that is how we *use* it in our "language".
(You are never going to actually get to 0.3...... by adding lots of numbers together; because it would take you infinitely long :P )
OP
OP
Deleted member 26715
Guest
100 lines "I need to keep my teaching on subject & within the scope of the audience"
I do numbers. Can i write out sqrt(2) as a continued fraction for 100 levels?
Drat, done it again, off topic ...
Profpointy
Legendary Member
This is the 5th page of a thread, and whilst somewhat off topic, it's more a "broadening" than a derail surely? Hey, no one's even mentioned Hitler yet
Beebo
Firm and Fruity
- Location
- Hexleybeef
Adolf had 2 balls but lost one in the Albert Hall.
how many balls does Adolf have now?
Before you can answer a difficult question like that, first you'd have to establish that 1+1=2
https://blog.plover.com/math/PM.html
