the most bizarre numbers - Scientific American

khansaheb said:
www.scientificamerican.com

These Are the Most Bizarre Numbers in the Universe

Most real numbers are unknown—even to mathematicians
www.scientificamerican.com www.scientificamerican.com
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Well! She boobed on her definition of the Rational Numbers!
She gave only Integer examples, omitting the likes of: ¼ ½ ¾ ⅓ ⅔ ⅛ ⅜ ⅝ ⅞ etc. and then said that: "The rest of the numbers on the number line are irrational numbers." ?

Otherwise an interesting read but for the most part doesn't it just tell us what most of us already knew and then goes on to consider the nature of Infinity (∞)?
 
The Highlander said:
Well! She boobed on her definition of the Rational Numbers!
She gave only Integer examples, omitting the likes of: ¼ ½ ¾ ⅓ ⅔ ⅛ ⅜ ⅝ ⅞ etc. and then said that: "The rest of the numbers on the number line are irrational numbers." ?

Otherwise an interesting read but for the most part doesn't it just tell us what most of us already knew and then goes on to consider the nature of Infinity (∞)?
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I think the definition is ok. The "include" part is a bit awkward:
"The rational numbers (that is, numbers that can be written as the fraction p⁄q, where p and q are integers) include the natural numbers (0, 1, 2, 3,...) and the integers (..., –2, –1, 0, 1, 2,...)."
If A includes B, C, D, technically, it's not a mistake to say A includes B and C.
 
lev888 said:
I think the definition is ok. The "include" part is a bit awkward:
"The rational numbers (that is, numbers that can be written as the fraction p⁄q, where p and q are integers) include the natural numbers (0, 1, 2, 3,...) and the integers (..., –2, –1, 0, 1, 2,...)."
If A includes B, C, D, technically, it's not a mistake to say A includes B and C. Can't argue with that!
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But when she said: "The rest..." that surely implies that although B & C are in A, D (specifically) isn't. ?
 
The Highlander said:
But when she said: "The rest..." that surely implies that although B & C are in A, D (specifically) isn't. ?
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Your grammar is lacking. Here's what the article says:

The real numbers are made up of the rational and irrational numbers. The rational numbers (that is, numbers that can be written as the fraction p⁄q, where p and q are integers) include the natural numbers (0, 1, 2, 3,...) and the integers (..., –2, –1, 0, 1, 2,...). The rest of the numbers on the number line are irrational numbers.
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"The rest" clearly means "every real number except what was just described, namely the rational numbers". It is not saying "everything except the subgroups that were mentioned in explaining the rational numbers".

Moreover, the definition of the rational numbers explicitly mentions fractions, so there is no need to mention them again. The point of mentioning natural numbers and integers is entirely to prevent the reader from thinking the rational numbers don't include them, as many might. They are not given as a list of typical examples illustrating what rational means, but as special cases not to be missed.

I suspect you are thinking that "include" means "consist of". It does not.

I imagine other readers besides you might misunderstand, so the wording could be improved a little. But this is not the gaffe you make it out to be.
 
The real numbers are made up of the rational and irrational numbers.
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The rational numbers......written as the fraction p⁄q......
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The rest of the numbers on the number line are irrational numbers.
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I think she wrote "the rest of the numbers" to mean the real numbers that are not rational.

She maybe included naturals (including zero) and integers as examples of rational because general population don't think of those as -1/1, 0/5, 2/2, etc.
 
Sorry for repeating Dr. Peterson's point. I just posted at the same time. ;)
 
I like the article; I'm glad it was posted. I knew algebraic and transcendental, but non-constructibles were not mentioned (and constructibles via compass glossed over), in my classes. Nice venn diagram.
realNumbers_graphic_3.png
 
Probably many people think of an irrational number such as pi (π) or Euler’s number. And indeed, such values can be considered “wild.” After all, their decimal representation is infinite, with no digits ever repeating.

I noticed the above. Aren't there just 10 digits? Pi has no digits repeating?! I of course know what the author meant to say.
I'm amused how a theoretical physicists gets to talk about bizarre numbers.
 
Steven G said:
Probably many people think of an irrational number such as pi (π) or Euler’s number. And indeed, such values can be considered “wild.” After all, their decimal representation is infinite, with no digits ever repeating.

I noticed the above. Aren't there just 10 digits? Pi has no digits repeating?! I of course know what the author meant to say.
I'm amused how a theoretical physicists gets to talk about bizarre numbers.
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Definition: The bizarre numbers are a subset of the real numbers, such that the number is not only transcendental but also related to Dr. Seuss, such as the bizarre number that represents the average amount of time it takes for a Noothgush to chase down a boy and stand on his toothbrush, called a noothgushtoothbrush. 1 noothgushtoothbrush is approximately 1.15 seconds, or about 1.54 bofagrapeseconds.

-Dan
 
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