I asked AI what is more - a million billion or a billion million

Depends rather on your definitions.

The originals were million, meaning 1000^2, billion = M^2 (bi means two), trillion = M^3 (tri means three, etc.; multipying from one million by one million (not one thousand) each time.

The American dictionary, perhaps driven by the money trade, removed the arithmetical link to make the billion = 1000 million instead. So the set of names lost their etymology hence numerical meaning.


Your sum is not quite correct though.

We add the indices, not the basic values, when multiplying by powers:

Using the arithmetical definitions as I think you have done:

I million X 1 billion = 10^6 X 10^12 = 10^(6 +12) = 10^18 = 1 million million million = 1 million cubed = 1 trillion.

This is identical to 1 billion X 1 million, because multiplications and additions can be expressed either way round.

It also shows the principle of Logarithms (here, to base-10).

Apparently the terms "billion" and "trillion" can each have 2 definitions, depending on the naming scale system used. Billion can either mean 10^9 (short scale) or 10^12 (long scale). "Trillion" can mean 10^12 (short scale) or 10^18 (long scale).

Short scale calculations:
million billion: 10^6 * 10^9 = 10^15
billion million: 10^9 * 10^6 = 10^15

Long scale calculations:
million billion: 10^6 * 10^12 = 10^18
billion million: 10^12 * 10^6 = 10^18

So if AI said a million billion = a trillion, it's using the long scale naming system (10^18).

You are also correct that a trillion = 10^3 * 10*9 = 10^12, if using the short scale naming system.

(This though..."10^12 + 10^9"... I don't understand how AI used that to calculate a trillion. To me that 10^12 + 10^9 = 1,001,000,000,000 or 1.001 * 10^12).

You must understand where most AI are deep learned. And that is usually the USA.

So the scales used are usually USA scales.

AI is very well known to make assumptions based on context as well. So it might give metric figures if you give it a hint.

Yet it's initial deep learning will always be USA based without any context.

Thats correct. Intuitively in words it looks wrong. But it is the same number of zeroes..😷