- #1

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## Main Question or Discussion Point

**I don't understand....**

These are things that I have tried looking up but still don't get it. What is..

1. Codomain

2. Morphism(homo, mono, iso, endo, auto, etc.)

3. Transfinite numbers

- Thread starter Skhandelwal
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- #1

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These are things that I have tried looking up but still don't get it. What is..

1. Codomain

2. Morphism(homo, mono, iso, endo, auto, etc.)

3. Transfinite numbers

- #2

CRGreathouse

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For another example, [tex]x\mapsto x^2[/tex] on [tex]\mathbb{Z}\rightarrow\mathbb{Z}[/tex] has domain Z, codomain Z, and range {0, 1, 4, 9, 16, ...}. The range could be equal to the codomain, but it's seldom expressed that way (because mathematicians prefer to use a 'major' or well-known set as the codomain, usually one of the blackboard bold ones. ).

- #3

matt grime

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1. Done.

2. A map. Homo means structure preserving, iso means invertible, endo means the domain and codomain are the same, i.e. a map f:X-->X, and auto is an invertible endo. All of these can be found simply by using google, by the way. If you have any more 'what is the definition' questions your first step should always be to use google to look them up (mathworld is a useful online resource). Of course, if you mean 'I have the definition but don't understand it' then it would be better if you wrote out what you think the definition is so someone can explain it to you.

3. The cardinals come with an arithmetic. The transfinite ones are those that are not cardinals of finite sets. E.g. Alpeh_0, c the cardinality of the continuum.

2. A map. Homo means structure preserving, iso means invertible, endo means the domain and codomain are the same, i.e. a map f:X-->X, and auto is an invertible endo. All of these can be found simply by using google, by the way. If you have any more 'what is the definition' questions your first step should always be to use google to look them up (mathworld is a useful online resource). Of course, if you mean 'I have the definition but don't understand it' then it would be better if you wrote out what you think the definition is so someone can explain it to you.

3. The cardinals come with an arithmetic. The transfinite ones are those that are not cardinals of finite sets. E.g. Alpeh_0, c the cardinality of the continuum.

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