I have always thought about how confusing infinity is... Is infinity equal to 0? My proof: Let infinity =a,a=2a, = a, a = 2a, so 0=a 0=a . - Is there something wrong with my proof? -Explain why you chose what you chose for #1.

Note by Genius Kid
3 weeks, 1 day ago

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I agree with @Zakir Husain. Infinity is not exactly a number. I like to think of infinity as "everything" and zero as "nothing".

However, if we're going to use either infinity or zero as numbers, like when doing calculations with other numbers for instance, we have to have special rules in place which will protect us from making a mistake.

For instance, though many would disagree, I would propose that rule #1 is:

  • x0=\frac{x}{0} = \infty

where xx is any number except 00.

And because of that condition, rule #2 would be:

  • 00\frac{0}{0} and \frac{\infty}{\infty} are undefined.

Here are the last few rules for working with 00 and \infty. Sometimes 00 behaves like \infty, but other times it does the exact opposite:

  • x+0=xx + 0 = x BUT x+=x + \infty = \infty (adding nothing to xx gives xx, BUT adding everything to xx gives everything)

  • x0=0x \cdot 0 = 0 AND x=x \cdot \infty = \infty (multiplying xx and nothing gives nothing AND multiplying xx and everything gives everything)

So in your original proof, it is impossible to subtract aa (\infty) from both sides and have 00 on one side, and \infty on the other. By rule 4, 2=2 \cdot \infty = \infty, so we would be left with 00 on both sides.

Hope this helps! Sorry if it was too long :)

David Stiff - 3 weeks ago

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genius kid - 3 weeks ago

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Your welcome! Just keep in mind that those rules are not ones mathematicians have formally agreed upon or anything. They're just basic math combined with my own propositions. :)

David Stiff - 2 weeks, 5 days ago

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I like your explanation.

Mei Zhan - 2 weeks, 5 days ago

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Thanks Mei!

David Stiff - 2 weeks, 4 days ago

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Infinity is not a number, it is a concept in mathematics. You can's treat it as a number.

Zakir Husain - 3 weeks, 1 day ago

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Yes, I agree. Plus this reminds me of the Numberphile video you shared. "types of infinity"

Mahdi Raza - 3 weeks, 1 day ago

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I always pictured infinity as the longest closed curve the real world of course

Sachetan Debray - 3 weeks, 1 day ago

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I don't think you can apply normal mathematics to infinity, As @Zakir Husain Sir said, \infty is not a number but a concept.

Vinayak Srivastava - 2 weeks, 5 days ago

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