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# Inference

**Inference** is a thought process were a conclusion is reached from premises.

## Contents

## Deduction

**Deduction** (deductive inference) is a type of inference where premises of a greater generality entail a conclusion of lesser generality.

### Syllogism

**Syllogism** is an example of deduction, e.g.

Premises:

*"All men are mortal"**"All Greeks are men"*

Conclusion:

*"All Greeks are mortal"*

Premises:

*"All Bs are As"**"All Cs are Bs"*

Conclusion:

*"All Cs are As"*

## Induction

Mathematical **induction**^{[1]} (inductive inference) is a type of inference where premises of a lesser generality entail a conclusion of greater generality.

### Weak induction

Mathematical [weak] induction is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers (positive integers). It is done by proving that the first statement in the infinite sequence of statements is true, and then proving that if the previous statement in the infinite sequence of statements is true, then so is the current one.

### Strong induction

Mathematical [strong] induction is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers (positive integers). It is done by proving that the first statement in the infinite sequence of statements is true, and then proving that if all previous statements in the infinite sequence of statements is true, then so is the current one.

## See also

## Notes

- ↑ Not to be confused with scientific induction.