Post me your hardest maths question you know

Mason- said:
You can't divide by infinity. It's not a number

let's divide 1 by cow.
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Exactly, so how can you take a concept and then say 100% that 0.9r = 1. 0.9r is 0.9 with an infinite number of trailing 9's.

If you take recurring to mean something other than repeating the number an infinite number of times then fine 0.9 does equal 1.
 
I can't believe people are claiming that 0.9r is equal to 1 !!!! So 0.99999 = 1??? Are you serious??? Where did you learn math, in a barn?































/gotcha!!!
 
fez said:
Exactly, so how can you take a concept and then say 100% that 0.9r = 1. 0.9r is 0.9 with an infinite number of trailing 9's.

If you take recurring to mean something other than repeating the number an infinite number of times then fine 0.9 does equal 1.
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You, like I was, are confusing the fact that infinity is not a number but a concept in that there is no limit.

For example, imagine there is no mavity at all and there is nothing at all.

You then jump (somehow) when do you stop? You wouldn't, neither does infinity.
 
Mason- said:
You, like I was, are confusing the fact that infinity is not a number but a concept in that there is no limit.

For example, imagine there is no mavity at all and there is nothing at all.

You then jump (somehow) when do you stop? You wouldn't, neither does infinity.
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I understand that concept, 0.3r will never stop growing but it will never get to the same value as 1.0r.

For 0.9r to === 1, you would have to at some point change that 0 in front of the .9r to a 1 or it will not be 1. If you do that then its not 0.9r as you are interfering and simplifying.

Involving conceptual ideas in mathematical proof seems like a bit of a sidestep to me. You can have an infinite decimal places but anything below 1 will never truly equal 1.
 
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fez, don't toy with infinity unless you understand what it is and what it means.

It's not an easy concept to grasp, and you have to be careful when dealing with it mathematically, so it's not surprising that you're having trouble with it.
 
growse said:
I really pray we don't get onto the differences between aleph-0 and aleph-1.

/cries
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Different infinities. That's fun. This isn't quite what you are talking about, but it's fun nonetheless.

A planet has two moons. Now imagine that there were an infinite amount of this system.

How many planets are there? An infinite amount.
How many moons are there? An infinite amount.

But, there are twice as many moons as there are planets.
 
fez said:
I understand that concept, but by that simple logic, any number with a recurring decimal is going to be infinitely large. 0.3r will never stop growing but it will never get to the same value as 1.0r.

Involving concepts in mathematical proof seems like a bit of a sidestep to me. You can have an infinite decimal places but anything below 1 will never truly equal 1.
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1/9 = 0.1r
9x (1/9) = 0.9r
9x (1/9) = 9/9 = 1.
ergo 0.9r = 1

?????????
 
Morbius said:
Different infinities. That's fun. This isn't quite what you are talking about, but it's fun nonetheless.

A planet has two moons. Now imagine that there were an infinite amount of this system.

How many planets are there? An infinite amount.
How many moons are there? An infinite amount.

But, there are twice as many moons as there are planets.
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But only 1 universe, which includes infinite planets and twice as many moons.

Hence 1> +oo and 1> 2x +oo

Problem? /trollface
 
Inquisitor said:
fez, don't toy with infinity unless you understand what it is and what it means.

It's not an easy concept to grasp, and you have to be careful when dealing with it mathematically, so it's not surprising that you're having trouble with it.
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Maybe thats the problem. We are looking at it from different viewpoints. As with most fields, they have their accepted truths that do not necessarily make sense outside of that field.

The way I see things like this is that the more precision you get, the less value each new unit of precision has. So if you have an infinite number of 9's after the point that you will always be getting closer and closer to 1.0r but you will never truly hit it. You would get to the point where the two were indistinguishable from each other but they would never truly be identical in value.

I was always taught that when we use recurring numbers that we are dealing in approximations rather than a precise value. I think that is where I am having the trouble.
 
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Fenris said:
No.

Clearly you know the answer to this, anyone with half a braincell does.

The men do not pay £9 each, the meal is £25 which you can't divide by 3, that is what screws up peoples thought process.

For anyone who has trouble with the question, think of it in terms of where the £30 they give to the waiter goes.

£25 - Till
£3 - Men
£2 - Waiters Pocket

There is no £9.
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3x10 paid = £30
3x1 refunded = £27 paid
+2 for the waiter =£29

If you gave me £10 and I gave you £1 back that means you paid me £9 correct? Much the same as if you gave me £30 and I gave you £3 back that would mean you paid £27. The waiter kept £2 for himself which added to the £27 would equal £29.
 
dmpoole said:
If you wrote 0.9 followed by an infinite number of 9s you would still have a sqillion gillion 9's (and then another squillion gillion 9's and so on).
It will never reach 1 and no amount of maths will prove otherwise.

HOWEVER, if some great Mathemeticians declared that the symbol 0.9r = 1 to make maths a bit easier then that is a different matter.
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Go read about infinity.

infinity does not mean a "squillion gillion"
 
w3bbo said:
3x10 paid = £30
3x1 refunded = £27 paid
+2 for the waiter =£29

If you gave me £10 and I gave you £1 back that means you paid me £9 correct? Much the same as if you gave me £30 and I gave you £3 back that would mean you paid £27. The waiter kept £2 for himself which added to the £27 would equal £29.
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think of it as here's 30 pound.
the meal costs 25 pound.
He gives 3 pound back from the 30.
30-3 = 27
He keeps 2 pound..
27-2 = 25.

Wow that was hard.
and to look at it like this:
each hyphen represents a pound coin.
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- meal
- tip
- tip
- pound back
- pound back
- pound back
 
w3bbo said:
3x10 paid = £30
3x1 refunded = £27 paid
+2 for the waiter =£29

If you gave me £10 and I gave you £1 back that means you paid me £9 correct? Much the same as if you gave me £30 and I gave you £3 back that would mean you paid £27. The waiter kept £2 for himself which added to the £27 would equal £29.
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Just have to remember that its only £25 paid. The fact that the 3 chaps have paid £9 each just means that you can see where the £2 tip has come from.

Paid £30 thinking that was right.
Discount takes their total to £25 meaning £5 to give back to 3 people.
Dodgy waiter decided that you would end up with all sorts of trouble doing this so pockets 2 quid out of the 5 and gives the 3 chaps £1 each.

You are no longer looking at a total of £30 having been contributed to the bill but £27. Seeing as the till only wants £25, there is 2 left for the light fingered parisian.
 
growse said:
Does that also mean pi can't exist?

After all, you can't write it down in decimal notation.

P.S. no-one with a suitably advanced education in maths asserts 0.9r!=1.
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no one above high-school maths ever needs to spend a single second thinking about 0.9r = 1


The issue is some people just can't comprehend concepts such as infinity.

It is no different to other series in maths, e.g. 1 + 1/2 + 1/4 + 1/ 8 + 1/16 + 1/32 .... +/n = 2 as n tends to infinity.
 
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