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Are there more real numbers than natural numbers between 0 and 1?

#31

@Cedur216 said in #27:

You're most definitely not a mathematician and you have no clue. The "continuum hypothesis" is undecidable within ZF/ZFC. You can take both the hypothesis and its opposite as an extra axiom and you have valid systems. That is no "proof".

I just read somewhere a proof that there are no intermediate cardinalities between rationals and reals. Let me see if I can find it.

@Cedur216 said in #27: > You're most definitely not a mathematician and you have no clue. The "continuum hypothesis" is undecidable within ZF/ZFC. You can take both the hypothesis and its opposite as an extra axiom and you have valid systems. That is no "proof". I just read somewhere a proof that there are no intermediate cardinalities between rationals and reals. Let me see if I can find it.
#32

Cardinality is not the same thing as size. The size of the reals is undefined because it's infinite, so while the sets have different cardinalities, the sizes aren't really comparable.

Cardinality is not the same thing as size. The size of the reals is undefined because it's infinite, so while the sets have different cardinalities, the sizes aren't really comparable.
#33

Well, there are infinite numbers between 0 & 1.
0<0.1<0.11<0.111<0.1111<0.11111 and whatever.
Bottom line is that there are infinity numbers between O and l.
Wait, did I say O & l? I meant 0 & 1.

Well, there are infinite numbers between 0 & 1. 0<0.1<0.11<0.111<0.1111<0.11111 and whatever. Bottom line is that there are infinity numbers between O and l. Wait, did I say O & l? I meant 0 & 1.
#34

From this entire disscussion i learned five things.

  1. Some people at this forum are funny (or think they are).
  2. There are pretty much people in this forum that are smart and like math (did everyone did go to university???).
  3. Google translate is bad at well... translating (deepl is better).
  4. There are many people who like maths (and for some reason they also listen in math lesson).
  5. So next time i am confused or got no clue i maybe shouldn't put it in the lichess forum. because first i got no clue about this and now i'm totaly bamboozeled (maybe i'm just too young...) .
From this entire disscussion i learned five things. 1. Some people at this forum are funny (or think they are). 2. There are pretty much people in this forum that are smart and like math (did everyone did go to university???). 3. Google translate is bad at well... translating (deepl is better). 4. There are many people who like maths (and for some reason they also listen in math lesson). 5. So next time i am confused or got no clue i maybe shouldn't put it in the lichess forum. because first i got no clue about this and now i'm totaly bamboozeled (maybe i'm just too young...) .
#35

@KevinWZG in which group would you "map" me?

@KevinWZG in which group would you "map" me?
#37

@KevinWZG what age / grade are you exactly? I'm a PhD in mathematics so I can be asked about any undergraduate stuff

@KevinWZG what age / grade are you exactly? I'm a PhD in mathematics so I can be asked about any undergraduate stuff
#38

first jeez phd in mathemathics!
second 13 years 8 grade in US?
live in the Netherlands de tweede klas.

first jeez phd in mathemathics! second 13 years 8 grade in US? live in the Netherlands de tweede klas.
#39

ok, pretty interesting (in a commendable sense) that you're engaging in such an advanced question (this was definitely no subject in my school time, only in first semester)

ok, pretty interesting (in a commendable sense) that you're engaging in such an advanced question (this was definitely no subject in my school time, only in first semester)
#40

so nevermind google translate was right.
The teacher asked the question wrong! correct is:
prove or disprove if there are more real numbers between 0 and 1 then there are natural numbers in total

so nevermind google translate was right. The teacher asked the question wrong! correct is: prove or disprove if there are more real numbers between 0 and 1 then there are natural numbers in total

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