1 day to go Part II

Αύριο τελειώνω!

Τελικά δεν απέχει πολλά η Δευτέρα που την Παρασκευή.

Math Analysis tomorrow…Ότι ξέρετε και σεις ξέρω και γω. Εν να μάθω 1000 πράματα πόξω, να πάω να τα γράψω και σε 5 λεπτά να τα ξεχάσω.


Prove that the irrational numbers are uncountable:

Since we know that Reals are the union of the rationals and irrationals we can deduce that irrationals are uncountable.
The rationals are countable since you can put them in an exhaustive ordered list which describes a bijection from the natural numbers to the set. Knowing also that the theorem which states that a union of countables gives a countable  set holds we can use it for contradiction.
The  Reals are uncountable as shown by the Cantor diagonal argument.
Hence if Reals = Rat. + Irr. we can deduce by contradiction that irrational numbers are uncountable.

Yup…τωρά που ξέρω ότι τα irrationals εν uncountable νιώθω καλύτερος άνθρωπος.


2 Responses to 1 day to go Part II

  1. anonymous says:

    eukola re !

  2. roam365 says:

    en je eipa oti en nen eukola. It’s a matter of remembering them. Γιατί δεν υπάρχει περίπτωση να ανακαλύψεις δικό σου proof τζινην την ωρα…

tsil to speak - comments

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