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Paradoxica

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Tbh I didn't memorise the latter. I was simply too lazy.

Besides those results...twist with maths too dangerously
The second one does not violate any known assumptions of high school mathematics.

The first one requires real analysis to justify.

The following number is clearly prime.

1000000000000066600000000000001
 

leehuan

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Honestly doubt I'll ever need the square root of 441 for real life.
Being able to deconstruct square roots is different. That's something different to being smart, that's being clever.
 

leehuan

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Oh whoops idk why I implied the second one did. But that was just cause way too many expressions. Hence lazy.
 

leehuan

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from the perspective of algorithmic complexity theory, squaring is easier than square-rooting.
I don't care about theory in THIS aspect. I only use neat tricks. It just so happens I haven't spent enough time on the trick for squaring.

for a sufficiently broad definition of "real life"...

Yes, the memorisation of identities will be more useful than mental arithmetic skills.
Save for one question - how?

If you just mean in the world of mathematicians that's different
 

leehuan

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wtf the first one, how is that a thing

isnt the second one just a typical limit?
You can't evaluate the second one by inspection or simple things alone so to speak. There's a really famous proof to it though.
 

Paradoxica

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I don't care about theory in THIS aspect. I only use neat tricks. It just so happens I haven't spent enough time on the trick for squaring.

You're still limited to square roots, cube roots and nth roots are a different matter.

Save for one question - how?

If you just mean in the world of mathematicians that's different
How is that different? It will be my life.
 

Paradoxica

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Lol. Your life is not congruent to our lives.
No, but it does fit the situation for which the argument is based on. My life, not anyone elses.

Because if you attempt to reword the question so that you're speaking for the perspective of everyone, that's just moving the goalposts.
 

leehuan

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How is that different? It will be my life.
Your life, is not everyone else's life. Your comments so far, being on the topic of mine, should refer to every single person, not just you. I was never talking about just my own life.

And for the record I don't bother with anything else other than square roots. I don't have that much time to invest into my arithmetic tricks like you with memorising algebraic identities.
 
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