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Random maths


davenportram

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I don't give a toss how much paints in a tin. I don't give a toss about which tins the heaviest. I don't give a toss about maths.

It's great not giving a toss, life's much simpler don't you think?- and if I ever need to work through an equation which will help me buy the cheapest carrots in Tesco, I just ask Dav. 'http://www.dcfcfans.co.uk/public/style_emoticons/<#EMO_DIR#>/wink' class='bbc_emoticon' alt=';)' /> 'http://www.dcfcfans.co.uk/public/style_emoticons/<#EMO_DIR#>/biggrin' class='bbc_emoticon' alt=':D' />

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The difference between them is infinitesimally small so it can be considered to be exactly 1

This is actually quite an interesting comment, but without clarification has absolutely no meaning. Define what you mean in a self consistent manner that is consistent with the real number line.

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This is actually quite an interesting comment, but without clarification has absolutely no meaning. Define what you mean in a self consistent manner that is consistent with the real number line.

As the professor at University told me

"Because if you write it in the real number line no matter how many nines you have there will always be another number between it and 1, so it never actually reaches 1. But the difference becomes so small it can be disregarded"

The same guy also said it its an inconvenience of the decimal system.

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Interesting thread, and I'd love to know what Albert's background with statistics is.

I think the 0.9999999 recurring is equal to 1, if you think about it graphically. Think about a curve tending to 1, and at the infinite point on that curve, it actually hits 1. The problem isn't the end of the sum, as it were - it's the concept of infinite. At the infinite point, 0.3333 recurring, x3, is 1. But you just can't get the concept of infinite into a puny human brain.

Nice questions though.

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Interesting thread, and I'd love to know what Albert's background with statistics is.

I think the 0.9999999 recurring is equal to 1, if you think about it graphically. Think about a curve tending to 1, and at the infinite point on that curve, it actually hits 1. The problem isn't the end of the sum, as it were - it's the concept of infinite. At the infinite point, 0.3333 recurring, x3, is 1. But you just can't get the concept of infinite into a puny human brain.

Nice questions though.

If a graph tends to a point it never actually hits it - the line it tends towards is an assymptote. Look at the the graph of y=1/x it tends to zero but never reaches it

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Interesting thread, and I'd love to know what Albert's background with statistics is.

I think the 0.9999999 recurring is equal to 1, if you think about it graphically. Think about a curve tending to 1, and at the infinite point on that curve, it actually hits 1. The problem isn't the end of the sum, as it were - it's the concept of infinite. At the infinite point, 0.3333 recurring, x3, is 1. But you just can't get the concept of infinite into a puny human brain.

Nice questions though.

Likewise the concept of something being infinitesimally small is a hard one to grasp, yet it us the key element of calculus and moving from the trapezium rule to show integration between limits giving the area under a curve.

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As the professor at University told me

"Because if you write it in the real number line no matter how many nines you have there will always be another number between it and 1, so it never actually reaches 1. But the difference becomes so small it can be disregarded"

The same guy also said it its an inconvenience of the decimal system.

Recurring decimals are a problem with the decimal system, but ultimately the argument that "no matter how many nines you have there will always be another number" argument is a flawed one.

Interesting thread, and I'd love to know what Albert's background with statistics is.

I think the 0.9999999 recurring is equal to 1, if you think about it graphically. Think about a curve tending to 1, and at the infinite point on that curve, it actually hits 1. The problem isn't the end of the sum, as it were - it's the concept of infinite. At the infinite point, 0.3333 recurring, x3, is 1. But you just can't get the concept of infinite into a puny human brain.

Nice questions though.

I'm not actually all that interested in statistics, although I have had a passing interest in them. I'm a PhD candidate in physics, and I just find maths in general quite interesting.

If a graph tends to a point it never actually hits it - the line it tends towards is an assymptote. Look at the the graph of y=1/x it tends to zero but never reaches it

Now, speaking about the graphs etc. is fun and all, but let's discuss this in a more exact manner. Sadly trying to write what I'm going to write into the forum as it is would look like a dog ate my formatting system, so I'll use another programme and post it as an image below:

0.999...=1 image

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A laymen with a mild interest in mathematics is never going to be able digest the extensive knowledge of mathematics you have, even if it's something you only find interesting. Your link above, I understand all the words and then you add those equations in and my brain boils.

You probably think you're dumbing it down, but it's still a mish mash of symbols and numbers to me.

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A laymen with a mild interest in mathematics is never going to be able digest the extensive knowledge of mathematics you have, even if it's something you only find interesting. Your link above, I understand all the words and then you add those equations in and my brain boils.

You probably think you're dumbing it down, but it's still a mish mash of symbols and numbers to me.

Yeah, it's hard to put it in simple terms... How about this:

When you have the number 0.999... and the number 1, for there to be a difference between the two there has to be a number between them. For example, take 0.9 and 1. There are many many numbers between them (there are actually infinite numbers between them). Examples of these are the average between them, 0.95, which is directly between them, but there is also 0.91, 0.92, 0.915... etc. If you take any two numbers that are different, there are infinitely many numbers that you can have between them.

Here's a silly example: I could take 0.4549552956210029872 and 0.45495529562100298721, and I could pick:

0.454955295621002987205

0.454955295621002987201

0.454955295621002987206

0.4549552956210029872001

0.454955295621002987209

0.45495529562100298720025568262549174562

...and it just keeps going, I can pick as many numbers between them as I so choose. Now, consider 0.999... and 1 again. Can you think of a number between them? It's 9s all the way, so I can't just chuck in any more decimals... Before we tried the average of the two numbers to find one between them, but as I did in that image I made, the average of 0.999... and 1 is actually 0.999..., that is, the average is the same as one of them. By definition this means that they have to be the same number. This is essentially what I was demonstrating, in an admittedly complex way by the end (or the start actually).

Hopefully that's understandable.

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