Frequently Asked Questions
What is Galileo's paradox?
There seem to be far fewer perfect squares than naturals, yet you can match each natural with one square: same infinite size. Galileo concluded that comparing infinite quantities by greater or less than is fraught.
Does this mean infinity equals infinity?
When we mean cardinality, yes - the naturals and the squares have the same cardinality, aleph naught. Cantor later showed not all infinities are equal: the reals have a strictly larger cardinality.
Are there more squares than primes?
Both sets are countably infinite, so they have the same cardinality. Their density among the naturals differs - square density falls like one over the square root of n, primes like one over log n - but cardinality is the same.
Provided by AllCalculators.io
Free online calculators for everyday. No registration required.
Estimates for informational purposes only.
Important Disclaimer: Estimates for informational purposes only.
This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.