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I was just thinking about how division by zero is undefined and began wondering if dividing by infinity is undefined as well. I understand the limits that accompany this idea [PLAIN]http://www4a.wolframalpha.com/Calculate/MSP/MSP194219b2befa7461g38e00003i7ih720ai6i1egc?MSPStoreType=image/gif&s=38&w=66&h=36 [Broken] and everywhere I look its defined as 0 but I came up with a little contradiction so to speak as follows

Assume these to be true:

A[itex]\neq[/itex]0

[itex]\frac{A}{\infty}[/itex]=0

Then,

[itex]\frac{1}{\infty}=\frac{0}{A}[/itex]

1=[itex]\frac{\infty*0}{A}[/itex]=0

1=0

Can someone explain this to me and why division by ##\infty## is 0?

Assume these to be true:

A[itex]\neq[/itex]0

[itex]\frac{A}{\infty}[/itex]=0

Then,

[itex]\frac{1}{\infty}=\frac{0}{A}[/itex]

1=[itex]\frac{\infty*0}{A}[/itex]=0

1=0

Can someone explain this to me and why division by ##\infty## is 0?

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