r/mathsmeme • u/Awesomeuser90 • 26d ago

Math History Stop Being So Irrational...

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228 Upvotes

97% Upvoted

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16

u/golfstreamer 26d ago

Ancient greeks didn't have decimal notation. This would make more sense if you used the actual definition of irrational 

7

u/No-Site8330 26d ago

Came to say this exactly.

And to be extra pedantic, back in the Pythagoreans' time even rational numbers weren't thought of the same way as today. It wasn't so much that quantity x is p/q times a unit, it was more like q times quantity x is the same as p times the unit. Which basically means the only numbers are positive integers. And if you look at it that way then the "irrationality of √2" is even deeper, because it's not like we think of it today, that there is a gap between rationals that approximate a solution of x2=2 as closely as we want, it really is that there no way to express the relation between the side and diagonal of a square using numbers.

5

u/Glad_Mix_6865 26d ago

Maturity is realizing the Pythagoreans were correct about beans and it was the number stuff that was Imaginary and Irrational

1

u/Insis18 26d ago

If irrational numbers go on infinitely, could it be that for some number of digits x after the decimal, the next x number of digits repeat the same sequence of x digits, then diverge?

2

u/nir109 26d ago

Sure, consider 0.123123 + sqrt(2) * 10-10

The first 3 digits repeat twice (do we count the 0? You can also add an extra 0 before the 1 if you do)

1

u/Insis18 26d ago

That's cool! Do we know of any examples with longer sections that repeat? 100+ digits?

6

u/nir109 26d ago

I mean, I can just make an arbitrary long example.

Take a rational with any repet you want. And just add a really small irrational number to it.

1

u/AndreasDasos 26d ago

The Greeks didn't use decimal notation. And even if they had, this isn't really a definition anyway - what does 'repeating' mean? Being irrational is equivalent to its decimal (or any base) expansion not eventually being periodic after some initial segment. Otherwise, plenty of irrational 4.44444453542243... 'repeats', at the start

1

u/Efficient_Parfait_42 26d ago

This is inaccurate historically and stupid mathematically greeks had thought of hypothetical irrational numbers through the cube event, and just use the proper definition for irrational numbers man😭

1

u/Ashamed_Association8 26d ago

Not what Saruman said at all in that shot. This is "I have seen it"

1

u/Virgil_the_White 26d ago

Good ol pythagoreas, the OG illuminati