How many rational and irrational?

Given any $2$ integers $a$ and $b$ where $a>b;a-b=d$ , what is more, numbers of rational numbers between them or numbers of irrational numbers between them?

#NumberTheory

Easy Math Editor

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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}`	$\boxed{123}$

Comments

I think irrational? I am not sure...

Vinayak Srivastava - 1 year ago

I think there will be an infinite number of rationals and irrationals

Mahdi Raza - 1 year ago

Infinities are also comparable, we have to see which infinity is bigger see here

Zakir Husain - 1 year ago

Nice video. Though I still don't know the answer to what is bigger in this case (rational or irrational)

Mahdi Raza - 1 year ago

@Mahdi Raza – I believe it actually may. James mentioned that the rational numbers (fractions) are "countably" or "listably" infinite. So we could, with an infinite amount of time, write them all down. However, the irrational numbers are "uncountably" or "unlistably" infinite, which means that even with an infinite amount of time, there would still be more numbers we had missed. So in a very odd sense, there would be more irrational numbers than rational. Though it seems much more intuitive to simply have one kind/size of infinity, since you can't have more than everything. :) @Zakir Husain

David Stiff - 1 year ago

@Zakir Husain: Check this out

Mahdi Raza - 12 months ago

@Mahdi Raza thanks!

Zakir Husain - 12 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}`	$\boxed{123}$