Full Idea
If we add ω onto the end of 0,1,2,3,4..., it then has a different length, of ω+1. It has a different ordinal (since it can't be matched with its first part), but the same cardinal (since adding 1 makes no difference).
Gist of Idea
ω + 1 is a new ordinal, but its cardinality is unchanged
Source
David Bostock (Philosophy of Mathematics [2009], 4.5)
Book Reference
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.110
A Reaction
[compressed] The ordinals and cardinals coincide up to ω, but this is the point at which they come apart.