Algebra uses rational numbers only.

Added: 2026-06-02

[00:00:01]Greetings, once again.

[00:00:03]Um I'm recording this short from a cafe where I normally well, not not always, but sometimes have a coffee.

[00:00:14]So, this is [clears throat] the place, just so that you know where I am.

[00:00:28]And right through the window there is the port.

[00:00:32]>> [clears throat] >> People are sitting outside smoking, that's why I'm sitting inside because they're not allowed to smoke inside. So, what I'd like [clears throat] to talk about today is >> [snorts] >> the fact that algebra deals only with rational numbers. So, for example, when one says a third pi times three, nothing actually happens with the symbol pi. It's just three times a third, so for all intents and purposes, pi has nothing to do with the calculation. The same thing happens when you have another constant like square root two and you square it.

[00:01:19]The operation is done entirely entirely on the index, okay? So, you could have cake underneath the radical and cake wouldn't be touched at all, right? So, algebra deals only with rational numbers and formalists have made a big mistake with the field axioms in saying that the multiplicative identity holds for all real numbers.

[00:01:46]Well, it can only hold for pi if pi is a label, not a number.

[00:01:52]And that's what they do. They say pi is equal to pi times one, not understanding what multiplication is.

[00:02:00]And so, yeah, they make a big mess up here as they have last 150 years.

[00:02:06]So, if you don't already subscribe to my channel, become subscriber, click like.

[00:02:11]And yeah, follow me on academia.edu. Till next time, I'm John Gabriel.

[00:02:19]Goodbye.