(mathematics) | aleph 0 - The cardinality of the first infinite
ordinal, omega (the number of natural numbers).Aleph 1 is the cardinality of the smallest ordinal whose cardinality is greater than aleph 0, and so on up to aleph omega and beyond. These are all kinds of infinity. The Axiom of Choice (AC) implies that every set can be well-ordered, so every infinite cardinality is an aleph; but in the absence of AC there may be sets that can't be well-ordered (don't posses a bijection with any ordinal) and therefore have cardinality which is not an aleph. These sets don't in some way sit between two alephs; they just float around in an annoying way, and can't be compared to the alephs at all. No ordinal possesses a surjection onto such a set, but it doesn't surject onto any sufficiently large ordinal either. |

Browse

Aleksandr Pavlovich

Aleksandr Porfirevich Borodin

Aleksandr Prokhorov

Aleksandr Scriabin

Aleksandr Sergeyevich Pushkin

Aleksey Maksimovich Peshkov

Aleksey Maximovich Peshkov

Alem

Alemannic

Alembic

Alembroth

AlenCon lace

alendronate

Alength

Alep

aleph

**-- aleph 0 --**

aleph-nought

aleph-null

aleph-zero

Alepidote

Alepisaurus

Alepole

Aleppa grass

Aleppo

Aleppo boil

Aleppo grass

Aler sans jour

Alert

alerting

Alertly

Alertness

Alessandro di Mariano dei Filipepi

Aleksandr Porfirevich Borodin

Aleksandr Prokhorov

Aleksandr Scriabin

Aleksandr Sergeyevich Pushkin

Aleksey Maksimovich Peshkov

Aleksey Maximovich Peshkov

Alem

Alemannic

Alembic

Alembroth

AlenCon lace

alendronate

Alength

Alep

aleph

aleph-nought

aleph-null

aleph-zero

Alepidote

Alepisaurus

Alepole

Aleppa grass

Aleppo

Aleppo boil

Aleppo grass

Aler sans jour

Alert

alerting

Alertly

Alertness

Alessandro di Mariano dei Filipepi