Do you think non-Euclidean geometry refutes Euclid's axioms? If so, how? If not, why not?

(December 10, 2021 at 2:34 am)vulcanlogician Wrote: Do you think non-Euclidean geometry refutes Euclid's axioms? If so, how? If not, why not?

Refutes? No. They show that Euclid's axioms are one possibility among many non-equivalent geometries.

If you assume Euclidean geometry, you can construct a model of non-Euclidean geometry inside. If you assume non-Euclidean geometry, you can construct a model of Euclidean geometry inside. The internal consistency of either implies that of both.

At that point, the geometry of 'real space' becomes a physics question and not a mathematics question.

Things start getting interesting when we get to the same phenomena in set theory: there are many different alternatives for set theory, many of which can be proved to be mutually consistent.

And, even more, there are multiple alternatives to *logic*, with standard two-valued logic only one of many possibilities (including paraconsistent logic).

All that means is that we get to choose which mathematical system we want to use to describe other things. Internally, we can study all of the alternatives.


BTW, I am not a Platonist. I am a Formalist when it comes to math.

I have a statment. I studied math in a poor country. And because nobody told what are practical use of particular part of the math and geometry, 95% failed math. Yes it is math isnt an easy topic, but it felt like a mindless programm.

Is 80085 the greatest number ever?

(December 10, 2021 at 10:54 am)purplepurpose Wrote: I have a statment. I studied math in a poor country. And because nobody told what are practical use of particular part of the math and geometry, 95% failed math. Yes it is math isnt an easy topic, but it felt like a mindless programm.

Educational systems, especially concerning math, are often very poor.

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(December 10, 2021 at 12:13 pm)no one Wrote: Is 80085 the greatest number ever?

Depends on whether it is a man or a woman delivering the lecture.

Who invented fractions?

(December 8, 2021 at 10:27 pm)polymath257 Wrote: I've been a research mathematician for the last 35 years. Any questions?

I'm not sure, but if my IQ test proves anything, it's that not all sneeps are fleebs.  

(December 10, 2021 at 12:45 pm)onlinebiker Wrote: Who invented fractions?

That actually has a rather long and complicated history.

The ancient Egyptians used a type of fraction, which we now call Egyptian fractions. In our system, an Egyptian fraction is one with 1 in the numerator: so 1/4 , 1/9, 1/23, etc, but NOT 2/23, 5/9, 7/15. They then expressed other fractions as sums of those. So, 2/5 = 1/3 + 1/15.

Decimal fractions, like .529 came much later. Obviously, the invention of the decimal system of numbers had to be created first. The first use of decimal fractions was in medieval Islamic areas, with al-Samawal usually given credit for these, although they may go back a bit further.

Decimals like we use them today, like 23/75, are later still, with the rules not completely worked out even in renaissance Europe.

Most people don't realize how recent many common mathematical concepts are. The idea of a 'number line' didn't arise until about 1000 AD.

(December 10, 2021 at 2:42 pm)polymath257 Wrote:

(December 10, 2021 at 12:45 pm)onlinebiker Wrote: Who invented fractions?

That actually has a rather long and complicated history.

The ancient Egyptians used a type of fraction, which we now call Egyptian fractions. In our system, an Egyptian fraction is one with 1 in the numerator: so 1/4 , 1/9, 1/23, etc, but NOT 2/23, 5/9, 7/15. They then expressed other fractions as sums of those. So, 2/5 = 1/3 + 1/15.

Decimal fractions, like .529 came much later. Obviously, the invention of the decimal system of numbers had to be created first. The first use of decimal fractions was in medieval Islamic areas, with al-Samawal usually given credit for these, although they may go back a bit further.

Decimals like we use them today, like 23/75, are later still, with the rules not completely worked out even in renaissance Europe.

Most people don't realize how recent many common mathematical concepts are. The idea of a 'number line' didn't arise until about 1000 AD.

Rrrrrrrrrrrrr

Wrong answer.


Henry the 1/8th


...


You expect serious?

What's the deal with 3, 6, and 9? (I think it's just about 3 but.........)

3x4=12, 1+2=3
6x24=144, 1+4+4=9
9x2025=18225, 1+8+2+2+5=18, 1+8=9
6x85069=510414, 5+1+0+4+1+4=15, 1+5=6
3x50647921=151943763, 1+5+1+9+4+3+7+6+3=39, 3+9=12, 1+2=3

Nonfunctional math guy is curious.