Math Investigation eTwinning. Mission: Infinity...Affairs! Volume: Infinity | Page 15

The Continuum Hypothesis
Georg Cantor (1845–1918) was the first mathematician to
realize that there are different kinds, different sizes of infinity.
He called these different sizes cardinalities. Cantor viewed his
mathematical discoveries in a very philosophical way and
believed that his study of infinity could explain the absolute
infinity of God. During his life, his research was dismissed as
‘shocking’ and ‘corrupting’, but it is fundamental to modern
mathematical logic.
We have shown above that , and all have the same
cardinality, which is called Aleph 0 and written as ℵ0 (Aleph is
the Hebrew letter A). We have also shown that the real
numbers have a bigger cardinality.
One question which Georg Cantor asked is whether the cardinality of is the next bigger
cardinality after ℵ0 (in the same way that 1 is the next bigger integer after 0). This is called
the Continuum Hypothesis. Cantor spent many years of his life trying to prove it – but he was
unsuccessful.
Only much later, in 1963, mathematicians discovered something very curious: The continuum
hypothesis could be true or false, and it is impossible to prove it either way. It basically means that
you can decide for yourself whether you want it to be true or not. The existence of unprovable
statements like the continuum hypothesis was discovered by Kurt Gödel.
Collaboration among greek and italian students teams
for the eTwinning project Math Investigation.
Activity: Infinity
Teachers: Katerina Atmatzidou and Matilde Aimetta

Sitography: http://world.mathigon.org/Infinity

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LYKEIO SCHIMATARIOY, GREECE

- VALLAURI FOSSANO, ITALY

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