Post me your hardest maths question you know

Morbius said:
If two real numbers are different, then you can always find a third number that sits between them.

What number sits between 0.9r and 1?
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I reckon it's a 9 between the 9 and the r which means I will NEVER reach 1.

If I wrote 0.9 followed by a gazillion trillion bagillion 9's I will still not reach 1.

Funnily enough I'm watching a BBC documentary called Beautiful Equations.
 
So simply put; in "real life" a number less than 1 is not 1. Mathematically, the concept of a decimal recurring to infinity allows this equality.

Maths != "real" life... :)
 
D.P. said:
wrong, you will hit the wall after n infinite time.

You just aren't understanding the concept of infinity.


You also seem to have believe that 0.9r is a different entity to 1.

0.9r means exactly the same thing as 1, it is just 2 different symbols that mean the exact same thing.
By definition, 0.9r = 1. This is absolute true in every sense of the meaning.

What you are arguing is 1 != 1. Which is just absurd.

1=1
1= 0.9r


0.9r does not mean 0.999999999999999999999999999999999999999999999999999.... with a very long repetition of 9s. 0.9r means 1.

Here is another example:
X = 1
Y = 1
X = Y. You are trying to argue that this doesn't hold, of course it holds, by the very definition. X and Y are just different symbols to represent the same thing.
Just because a number has two different symbolic representation doesn't mean they are different.


Its like giving someone a nickname, when you use their full name or their nickname you still refer to the same person, not two different people.
Click to expand...

Could you provide a link to show that this is correct? Thanks. Oh, a worthwhile link which absolutely proves this, please.
 
On the reals, two numbers, a & b are different if there exists some epsilon such that b is not in (a, a + epsilon) where epsilon -> (tends to) 0.

such an epsilon does not exist for 0.9r and 1.0, therefore they must be the same ;)
 
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This thread makes my head want to explode. I HATE maths so much, numbers make my head hurt!

I don't even know what square root means. I managed a B at Maths for GCSE but only because of the school I went to, even then I was in the bottom group.
 
dmpoole said:
I reckon it's a 9 between the 9 and the r which means I will NEVER reach 1.

If I wrote 0.9 followed by a gazillion trillion bagillion 9's I will still not reach 1.

Funnily enough I'm watching a BBC documentary called Beautiful Equations.
Click to expand...

yes, but if you wrote 0.9 followed by an infinite number of 9s you would reach 1.
 
AJK said:
So simply put; in "real life" a number less than 1 is not 1. Mathematically, the concept of a decimal recurring to infinity allows this equality.

Maths != "real" life... :)
Click to expand...

0.9r is not less than 1, it is 1.
You can call a limitation of the decimal point if you will. =.9r and 1 are exactly the same entitiy
 
i like this 0.9r = 1 debate.

Seems its a relatively recent concept, maybe why lots of people don't swallow it so easy.

I personally never came across it being taught at school or higher education so find it to be like a mental block, maybe this is why i despised maths for the sake of maths.
 
From my physics undergrad... Can't believe I used to be able to do this :p

quantum.GIF
 
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