Questions tagged [numbers]

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Were Ten and One Hundred Thousand treated more like "special" numbers at one point than today?

Note: Not English specific but about any major system of recording or discussing numbers. I know some systems would not give 100 a special place. People today when discussing largish numbers tend to ...
releseabe's user avatar
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4 votes
2 answers
766 views

When and why was the concept of "having a least upper bound" dubbed "completeness", as in Axiom of Completeness?

The Axiom of Completeness states that any non-empty set with an upper bound has a least upper bound. When and why was this concept of least upper bound dubbed "completeness"? It's true, of ...
SRobertJames's user avatar
2 votes
0 answers
114 views

I would like to read about Euler's view on negative numbers

So, I've been over fixated on negative numbers lately. I'm coming to the conclusion that, mathematics is usually progressed if it is "useful". The more "useful" a mathematical ...
Demon's user avatar
  • 63
0 votes
0 answers
113 views

How did negative numbers “force themselves” onto Cardano, and was it analogous to how imaginary numbers were forced upon him?

I was reading “A brief history of numbers” by Corry, but I came across a part that confused me. Cardano accepted the law of signs for “subtractions” proposed by an older group of Italian ...
Fraser's user avatar
  • 21
0 votes
2 answers
273 views

How was addition and multiplication of natural numbers defined before 1870 (Cantor and modern set theory)?

I know how to define addition and multiplication of natural numbers using set theory, but I think that before Cantor, mathematicians did not try to use set theory as a foundation for mathematics (I ...
pie's user avatar
  • 263
3 votes
0 answers
152 views

How did Hindu-Arabic Numerals get their shapes?

I’ve noticed a recurring post on social media that presents an image suggesting the shapes of Hindu-Arabic numerals are connected to the angles within their design: This claim seems dubious to me. I ...
Humberto José Bortolossi's user avatar
2 votes
1 answer
197 views

Did Fibonacci not grasp the idea of zero?

Indian mathematicians (e.g., Brahmagupta in the 6th century) developed the idea of 0 as more than a placeholder. In 1202, Fibonacci wrote "These are the nine figures of the Indians: 9 8 7 6 5 4 3 ...
user19226's user avatar
1 vote
1 answer
91 views

When was the first time the number 0 came to mean a multiple of ten? [closed]

The earliest number notation I can find is the sexagesimal digit notation of cuneiform. From my understanding of that, in order to make numbers bigger than 60, you would just add the smaller numbers ...
Curious Layman's user avatar
4 votes
0 answers
123 views

Terminology associated with mathematical induction

In "Number: The Language of Science" (1930), Tobias Dantzig refers to what we call the base case of mathematical induction as "the induction step" (and refers to what we call the ...
James Propp's user avatar
4 votes
0 answers
123 views

Did the ancient Greeks know that "most" cube roots are irrational?

It is common knowledge that the Pythagoreans discovered irrational numbers (or incommensurability), for example if the hypotenuse of an isosceless right triangle is compared with one of the legs or ...
Frunobulax's user avatar
2 votes
2 answers
601 views

Gate 44 at the Colosseum in Rome: XLIIII or XLIV? When and why the change?

We teach our children in school that 4 is written in Roman numerals as IV and not as IIII but at the Colosseum in Rome, gate 44 is identified as XLIIII and not as XLIV. When did the change from IIII ...
Humberto José Bortolossi's user avatar
1 vote
0 answers
102 views

Why have advocates for positional number systems based on divisibility favoured base 12?

In the early twentieth century, with Esperanto and the like going on, a small movement called "dozenalism" began, with the aim of replacing base 10 with the purportedly more natural base 12. ...
Thomas Anton's user avatar
0 votes
0 answers
89 views

Origin of Catalan numbers and original intuition of the first interpretation and proofs

I was reading about Catalan numbers and how they provide the number count in a variety of situations. I found it very interesting how the main proof is about the underlying common patterns and ...
Jim's user avatar
  • 111
0 votes
0 answers
63 views

Are there examples of mathematical systems that reflect the worldview of the culture they are from?

By this I mean, are there systems of numbers, counting, sorting.. or even higher level mathematical concepts that reflect a culture's worldview? Did some cultures not develop certain math concepts ...
Hypatia's user avatar
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0 answers
78 views

What was the difference between Number and Magnitude in Ancient Greece [duplicate]

I've been reading Infinite Powers by Steven Strogatz and in it, he writes about how the greeks differentiated between numbers as being discrete and magnitudes as being continuous. However, all of ...
user avatar
6 votes
1 answer
930 views

Historical origin of commas and periods in numbers

I have heard that in Canada and the United States of America, when we write a decimal number, then we use a period, like 1.111. When we write large numbers, then we use a comma, like 1,111. Sometimes ...
Arunabh Bhattacharya's user avatar
10 votes
2 answers
3k views

Why do South Asians often use "lakhs" and "crores" instead of "millions"? What is the historical origin of this system?

I noticed that South Asians often write 10,00,000 instead of 1,000,000. My questions are: What is the origin of this special numbering system? Was there a more practical reason for having a special ...
Arunabh Bhattacharya's user avatar
2 votes
1 answer
558 views

Was there ever a word for 24 like "dozen" for 12? [closed]

The English language has more than one word for 12 (twelve, dozen) and 12^2 (one hundred and forty-four, gross), but has there ever been a word for 2*12 other than twenty-four? I would also be ...
Improve's user avatar
  • 171
0 votes
0 answers
75 views

Has any culture in history ever not invented digits, and just used letters?

We have characters for letters and numbers. We typically view them as a discrete sets. Has any culture ever mangled the two? To some degree it seems almost logical if your letters are already ...
Evan Carroll's user avatar
10 votes
1 answer
263 views

When did the word "Real number" begin to be used as an official terminology to refer to both rational and irrational numbers?

I am really curious about and struggling with finding when the word "Real number" began to be used as an official terminology to refer to both rational and irrational numbers. In Wiki, it ...
withgrace1040's user avatar
4 votes
2 answers
321 views

Why did the romans use IV and why doesn't it overcomplicate things?

Ok so if the Romans did not use things like IX and IV and XC etcetera then addition and subtraction would be almost as instant as it is in our number system. However with the new system it seems to me ...
user avatar
1 vote
1 answer
124 views

Did anyone ever propose a hypercomplex numbers system with more than one anisotropic axis?

The real number axis is asymmetric against zero: for instance, multiplication of two negative or two positive numbers will produce a positive number, a square root of a negative number is not real, ...
Anixx's user avatar
  • 652
2 votes
1 answer
234 views

Who is the Dottie number named after?

I have learned about the Dottie number, though I am unsure to whom it is attributed to and why it is named as so.
aitía's user avatar
  • 139
0 votes
0 answers
101 views

Who invented the first pronunciation system for binary numbers that is roughly analogous to how we pronounce everyday decimal numbers?

Who invented the first pronunciation system for binary numbers that is roughly analogous to how we pronounce everyday decimal numbers (by which I mean how 220 is pronounced 'two hundred twenty')? ...
Matthew Christopher Bartsh's user avatar
13 votes
3 answers
5k views

Why are quaternions more popular than tessarines despite being non-commutative?

Is this simply because of marketing, hype, etc? The bicomplex numbers (especially tessarines) look just great being commutative and all. Images source:https://citeseerx.ist.psu.edu/viewdoc/download?...
Anixx's user avatar
  • 652
2 votes
1 answer
292 views

Has the idea that the result of division of positive number by negative number should be negative ever been controversial?

If we divide a positive number by another positive number, the result becomes greater as the divisor becomes smaller. If we continue this logic, division by a negative number should be greater than ...
Anixx's user avatar
  • 652
3 votes
3 answers
4k views

What is the origin of Arabic numerals

I was taught that the numerals {0,1,2,...,9} are from the Arabic alphabet. But they look completely different from today's Arabic letters. I wonder what is the origin of Arabic numerals? Edit: The web ...
Eugene Zhang's user avatar
6 votes
3 answers
1k views

Was the concept of zero ever developed without relation to positional number systems?

Are there any ancient civilizations which had concept of zero but didn't not use positional numerals for any somewhat non-negligible (from historical point of view) amount of time? If there are such ...
Vlad's user avatar
  • 163