Quick question about cardinals

  • Thread starter Dragonfall
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In summary, the conversation discusses how to define an uncountable set of cardinal numbers. One person suggests that every set of cardinals "up to x" seems to be countable, but the other person argues that there are uncountable ordinals, which also define uncountable cardinals. This implies that not all cardinals are countable.
  • #1
Dragonfall
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Assuming we define the cardinal number for a set A as the least ordinal number b such that A and b are equipollent, how would you define an uncountable set of cardinal numbers?
 
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  • #2
It's just an uncountable set. That it happens to be a set of cardinals is immaterial.
 
  • #3
What I mean is that under this model every set of cardinals "up to x" seems to be countable. So how to define an uncountable one?
 
  • #4
How does that imply that all cardinals are countable? Why not post a proof of that statement if it 'seems' to be so. Hint, let w be an uncountable ordinal. Such exist. It is not in bijection with any countable initial segment, so it must define an uncountable cardinal too.
 
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1. What are cardinals?

Cardinals are a type of bird that belong to the family Cardinalidae. They are known for their bright red plumage and are commonly found in North and South America.

2. How do you identify a male cardinal from a female?

Male cardinals have bright red feathers, a black mask around their eyes, and a crest on their head. Females, on the other hand, have a more muted reddish-brown color with a few red accents and a crest as well.

3. Do cardinals migrate?

Yes, cardinals are able to migrate, but it is not common for them to do so. They usually stay in the same area year-round unless food sources become scarce.

4. What do cardinals eat?

Cardinals are primarily seed-eaters, but they also consume insects, fruits, and berries. They often use their strong beaks to crack open seeds and nuts.

5. Can cardinals be kept as pets?

No, it is not recommended to keep cardinals as pets. They are wild birds and require specific diets and environments to thrive. It is also illegal to capture and keep wild birds as pets in many places.

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