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Hi,
This is because the two numbers do not live in the same ground field as you can see
sage: 1.414.parent()
Real Field with 53 bits of precision
sage: sqrt(2).n(digits=4).parent()
Real Field with 17 bits of precision
1.414 is not exactly represented in memory because it is not a diadic number. Two different diadic approximations with different precisions are different.
Vincent
