What does it mean to be unique up to isomorphism?

Unique up to isomorphism means that all the objects satisfying a given definition are isomorphic, or have the same structure. Less formally, it means that they are the same object with different names for things.

Is unique up to isomorphism?

To say that initial algebras are unique up to isomorphism means that they are all equivalent to each other with respect to the equivalence relation of isomorphism.

What does unique up to mean?

This figure of speech is mostly used in connection with expressions derived from equality, such as uniqueness or count. For example, x is unique up to R means that all objects x under consideration are in the same equivalence class with respect to the relation R.

What does isomorphic up to mean?

Simply put, we say two groups (or any other algebraic structures) are the same “up to isomorphism” if they’re isomorphic! In other words, they share the exact same structure and therefore they are essentially indistinguishable.

What does upto mean in inequalities?

2 Answers. 2. When one says “X is true up to Y”, then one means that it is not strictly speaking correct that X is true, and the Y which occurs after the up to clarifies the sense in which X is not quite true. Thus it really means “Roughly speaking X is true, except for Y”.

What does to be up mean?

1. To have arrived or have been placed at a high or higher position or location.

Are all Bijections Isomorphisms?

Every isomorphism is a bijection (by definition) but the connverse is not neccesarily true. A bijective map f:A→B between two sets A and B is a map which is injective and surjective. An isomorphism is a bijective homomorphism.

Does up to mean less than?

Meaning of up to in English. used to say that something is less than or equal to but not more than a stated value, number, or level: Up to two hundred people were on board the ship.

Is up to greater than or equal to?

Greater Than or Equal To Application

Symbol	Example	Meaning
Greater than or equal to, ≥	x ≥ 2 2 ≥ x ≥ −1	The value of x is greater than or equal to 2. The value of x should between −1 and 2 inclusive of both values.

Is ended up correct?

End up: is the end result of something in abstract thinking. Or end of something: that’s the end of the movie not at or up for these would change the entire meaning of the phrase. Example: we had an argument and eventually we ended up hitting each other. —The game ended at 5pm yesterday.

How did you end up meaning?

1. tiffy 7350. “How did you end up there?” or “How did you get here?” are basically the same. end up is a phrasal verb that means to reach a particular place or achieve a situation after other activities: *just think of “end up” as a result or a consequence of something.