#Real numbers

[math-memes]

[jadagul]

Just found out about another set of number: algebraic periods, a countable ring between the algebraics and the complex which includes many popular transcendental numbers.

Oh yeah, periods are lurking in the background of a lot of my PhD research but I never wound up focusing on them.

The big thing there is, you can add in any finite (or, I think, countable) set of transcendental numbers and still stay in a countable set. So just "what about pi?" isn't a good explanation of why the reals; you could use the algebraic numbers plus pi (and e), or whatever.

Which is why I focused, not really on the existence of pi, but on the sort of argument that produces it. If you stick to a countable set you could have pi, but you won't be able to make that sort of limiting argument reliably.

[sahanmagazine]

Real numbers

Definition

A number is called a real number , if and only if it is either a rational number or an irrational number. The set of real numbers, denoted by R, canbe described as the union of the sets of rational and irrational numbers.

R = ( x : x is a rational number or an irrational number. )

R = Q ∪  “Q prime” where rational numbers ( Q ) and irrational numbers ( “Q prime” ) Subsets of real numbers

All real numbers except complex numbers are real numbers. 

Therefore, real numbers have the following five subsets :

[nathaniacolver]

arcane ships be like

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If Wealth Was Evenly Distributed Across America, How Much Money Would Every Person Have?

This, btw, is the nw/income threshold to enter "middle class" — I can tell you're all lower-class poors because you're on Tumblr instead of having staff to do it

[technically-human]

He did eventually sign it

[utilitycaster]

"why should I get invested in shows if they'll just get canceled" I was deeply invested in Heroes (2006) and it was not canceled, it just got really terrible. I also got really invested in the sandwich I had a few weeks ago despite it only lasting like 15 minutes. You must embrace the ephemeral. You must be willing to love things that may not love you back, that might betray you, or that may die an untimely death. As the great philosopher Mr. Mitchell Lee Hedberg said "I'm not gonna stop doing something because of what happens at the end."

[fuckboispiderman]

Can anyone here count to 12 I keep getting lost at 13

[akanemnon]

Despite everything, it's still you.

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[jadagul]

In your Fictional History of Numbers, Part 3, you say that the probability of a randomly selected real number being rational must be 0, because if it were any 1/n then the reals would be in correspondence with the rationals and therefore countable. Does this follow? Why can't the probability be some irrational real? (I mean, I know that it is 0, and I intuit that it must be smaller than 1/n for any n, but it's not obvious to me that this is the basis for a rigorous proof.)

Yeah, I agree it's not rigorous. (It's a general audience piece!) The detail you have to fill in is: if the probability is some real number 0<r<1, then we can find a rational n such that 1/n < r < 1/(n+1), and then you can divide the reals up into n sets, each of which is the cardinality of the rationals. (And all of that requires some extra justification about, like, measure being invariant under translation etc. but again general audience piece.)

Also, the paragraph beginning "The reals are ordered" is kind of confusing, because it uses the adjective "ordered" in a way which can be read ambiguously as 'ordered (set)' or 'ordered (field)'. The first sentence seems to define "ordered" as 'ordered (set)'; the third sentence notes that the 'ordered (field)' properties are satisfied but doesn't read like part of the definition; the fourth sentence only makes sense if "ordered" means 'ordered (field)'.

Yes, I'm being a little imprecise there, because I think it flows better narratively. But yeah, the important claim is that the reals are ordered in a way that's compatible with the field axioms.

[sahanmagazine]

Decimals

                               

A decimal number can be described as a numeral whose integer part and the fractional part are separated by a dot.

The dot in a decimal number is called a decimal point. The digits after the decimal point show a value smaller than one.

         Converting fractions into decimal numbers

Toconvert a proper fraction ( denominator is greater than the numerator ) into decimal number perform the ordinary division process by dividing the numerator by the denominator, the result will be a decimal point, as shown below.

Fraction form Decimal form

  1/2                                  0.5

  1/4                                  0.25

  3/10                                0.3       

  1/5                                  0.2

  6/10                                0.6

            Converting  decimal numbers into fractions

To change a decimal number into a fraction, look the number of digits at the rightof the decimal point, for :

1) 1 digit only remove the decimal point and divide the number by 10.

2) 2 digits remove the decimal point and divide the number by 100

3) 3 digits remove the decimal point and divide the number by 1000.

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[alliekitaguchi]

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[wizard-loving-wizard]

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