0.9 recurring=1 (1 Viewer)

[Carrotsticks]

I don't really see what the problem is.

Most of those arguing against this accept the 'Limiting Sum' formula, but appear to be rejecting the idea of 0.9999... = 1, when it is actually the exact same concept.

The result can be proved trivially using a Geometric Series argument or even one using Cauchy Sequences.

The reason why this works is because we have INFINITE 9's, not finite. When introduced to the concept of infinity, things get a whole lot different.

ie: Why can you bracket finite terms and manipulate the commutative law of addition, but not do so with infinite terms?

This article may clear a few things up: http://en.wikipedia.org/wiki/Riemann_series_theorem

 

[seanieg89]

I don't really see what the problem is.

Most of those arguing against this accept the 'Limiting Sum' formula, but appear to be rejecting the idea of 0.9999... = 1, when it is actually the exact same concept.

The result can be proved trivially using a Geometric Series argument or even one using Cauchy Sequences.

The reason why this works is because we have INFINITE 9's, not finite. When introduced to the concept of infinity, things get a whole lot different.

ie: Why can you bracket finite terms and manipulate the commutative law of addition, but not do so with infinite terms?

This article may clear a few things up: http://en.wikipedia.org/wiki/Riemann_series_theorem

Agree with you obviously, but don't really see how the rearrangement of conditionally convergent series relates to this...

 

[Carrotsticks]

Agree with you obviously, but don't really see how the rearrangement of conditionally convergent series relates to this...

Oh, it was to emphasise how dealing with infinity totally changes things, as per the case of conditional convergence and how re-arranging terms (appropriately) can make the series converge (or diverge) to a whole different value.

 

[4025808]

While something related:

 

[Carrotsticks]

Isn't that just showing that 4 is an upper bound for pi?

If you really want to 'approximate it', we should consider the 'hypotenuse' of these 'square' things...

 

[lolcakes52]

I know, its obvious to anyone who watches it that she isn't being serious in the video.

 

[Riproot]

Im pretty sure that approaching something doesnt mean its equal or indistinguishable

but that just means not

Note: I know nothing about LaTeX
(my stats tutor called it L-Tex during our last tutorial and I was like "wot?")