It is "0" or "∞".

Let us consider some equation such as,

0 + 0 = 0 And, ∞ + ∞ = ∞

0 - 0 = 0 And, ∞ - ∞ = ∞

a * 0 = 0 And, a * ∞ = ∞

0/0 = { set of all real numbers or it is not defined } And, ∞/∞ = { set of all real numbers or it is not defined }

What this shows, Is zero is infinity or infinite is zero. If it is there should me no number line it should be a closed curve.

#NumberTheory

Easy Math Editor

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Comments

Well, $\infty - \infty$ is indeterminate not $\infty$ as you wrote.

Also, are you sure $a \cdot \infty = \infty$ ?

Vilakshan Gupta - 3 years, 5 months ago

Ya it is so, we know that ∞ + ∞ = ∞ and by taking a ∞ to RHS it becomes ∞ - ∞ = ∞ . and well I also think it is indeterminate but when we can't determine it what it can be. This shows that we have a lack of numbers and the number line what we think really exist is only the part of the unknown number line. One evidence to this is the complex numbers.

Ya I am sure that a*∞ = ∞

And this note is only for thinking above where we are, because thinking can change our view of learning. So carry on thinking .... √-1 where it is in number line. What is the value of 0 and that of ∞.

Sparsh Gupta - 3 years, 5 months ago

$\infty$ is not a number that you are taking it to right hand side. If that is so,I can claim that $\infty-\infty=0$ because $\infty=\infty$ and taking any $\infty$ to RHS or LHS , you will get the result.

How do you know that $a$ is positive ? If it is positive , then only $a \times \infty =\infty$ . If $a$ is negative , then $a \times \infty= -\infty$ and if $a=0$ , then $a\times \infty$ is again indeterminate.

Vilakshan Gupta - 3 years, 5 months ago

....😯😯

Ssss Dddddc - 3 years, 5 months ago

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}`	$\boxed{123}$