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what is the difference between countless and countably infinite

Countless just means a number that is beyond one's capabilities of counting...the number can be infinite or a very absurdly large finite number which is unknown.

As far as countable and uncountable infinity is concerned...
Refer to this...
 
Countless simply means there are too many to count, but may not be infinite.

Countably infinite means that there is some statement or measure which confirms the number is infinite.
 
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