Unsolved Questions - 1 - Hasna Hassen

The Mystery of Zero I recently got to know that some questions related to zero don't have any answers yet! Brahmagupta, a great mathematician in India, founded the number of zero in the 7th Century and made many rules when using that number, the results when you add, subtract and multiply zero by any number. But when it came to DIVIDING any number by zero... Well, he didn't give a solution. Later on Bhaskara, another mathematician in India stated that zero divided by a number would mean infinity! Then George Berkeley proved that was wrong saying that zero x infinity would mean any number, which I agree with. Time passed by, and the answer to that question was to be solved, and it just died out. But more questions came out, what was the result when you divide zero by zero? Normally it's one, but does zero have the same result too? Why is it considered as a real number then? I believe that people are really curious to find the correct answers which include you and me. So if you have any more information on my topic, just drop a reply. If not, just share your thoughts below! :)

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
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https://brilliant.org/discussions/thread/infty-infty/ That's a nice definition for infinity, which could have potential ;) (even if it hurts the field axioms)

CodeCrafter 1 - 1 year, 6 months ago

I thought about it the exact same way!

Hasna Hassen - 1 year, 2 months ago

That's fascinating Hasna that mathematicians in India were pondering this question. And I would actually agree with Bhaskara (as it turns out, the discussion CodeCrafter linked to is one that I wrote!).

However, I would also agree with Berkeley, that $0\cdot\infty$ is undefined. Here's how I reconcile the two:

$\frac{1}{0}=\infty$

BUT

$1\neq0\cdot\infty$

because to get this result, we would have to multiply both sides of the equation by $0$ . However, this is not mathematically defined, since multiplying $0$ by $\frac{1}{0}$ , results in either $\frac{0}{0}$ or $0\cdot\infty$ , both of which I would propose are undefined (and equal).

Thus, division by zero is indeed defined, but $0\cdot\infty$ (and $\frac{0}{0}$ ) is not. We cannot derive one from the other with defined mathematical operations either.

Hope this helps!

David Stiff - 1 year, 2 months ago

I was thinking about this, but I got confused when it came to 0/0, because then again in my post, there wasn't an answer. But when you told me about 0 into infinity, things looked a bit more clearer. So thnx! :) Oh and go check out my other post, "Unsolved Questions-2"

My question may look stupid, but what exactly is your definition of infinity?

Avyukta Manjunatha Vummintala - 1 year, 1 month ago

Your question wasn't stupid, you made me think deeper than ever to find the answer to your question! Speaking of answers, as every one knows, infinity is an endless number - whuch gives me a new definition that it's a number with no value. But on the second thought, we can't say "no value" caz zero has no value. So since infinity is endless, according to my opinion, infinity is a number with the highest value, and nothing is above it. This was my opinion, how about yours?

Hasna Hassen - 1 year, 1 month ago

@Hasna Hassen – Well, I came up with a definition( It might not be perfect) but it is: "Infinity is equal to the sum of 'biggest number you know' and 1."

@Avyukta Manjunatha Vummintala – And one? Oh so you mean "The biggest no. in the universe"+1? Was that what you meant?

@Hasna Hassen – Sort of. You see, the idea is that ' the biggest number you know' is constantly changing( i.e. going further and further towards the left on the number line). This definition helps in defining infinity in limits, but forbids any integration into an algebraic equation.

@David Stiff Actually, the number system you're writing in now was created by Indians. Many pondered zeros and infinities, but it is ancient Indian astronomers and mathematicians credited for assigning a number to nothing.

Krishna Karthik - 5 months, 3 weeks ago

Oh yes, that's right! It's funny when you think that there was a time when people didn't think of zero as a number!

David Stiff - 5 months, 3 weeks ago

@David Stiff – Yeah. It's actually quite cool how it's used as a placeholder in number systems, like our very own decimal system. I wonder what was used as a placeholder before zero was invented as a numerical value...

Anyone else for a definition for infinity? It would be nice to share your ideas!

@Avyukta Manjunatha Vummintala - Hmm. That makes sense. But sometimes when I get fed up finding the proper answer, I get the thought that since infinity is endlesss, maybe it's not a number at all! ;)

Well, I don't think that a definitive answer is found.

'The Hilbert's paradox' might interest you.....

Where can I find that? What's it about?

@Hasna Hassen – It is a paradox regarding infinity.

You can read about it here - https://en.m.wikipedia.org/wiki/Hilbert%27sparadoxoftheGrand_Hotel

It is often called "Hilbert's paradox of the grand hotel".

@Avyukta Manjunatha Vummintala I'm still 13, and that's a lot to read and understand! Maybe in a few days time, I'll go through it and comment about it.

@Hasna Hassen Brahmagupta did not invent zero, it was Aryabhatta.

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$