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donglepuss
- 17
- 4
find me an integer that isn't divisible by 1.
what do you mean?fresh_42 said:This is a contradiction in itself. ##1## is a unit.
No. Why would you think it is?donglepuss said:Is every integer derived from 1?
The statement that "1 is a unit" comes from a generalization of the notions of addition and multiplication into abstract "rings" The notions of divisibility and of being a "prime number" can apply to such structures. The notion of a "unit" is also definable.donglepuss said:what do you mean?
Have you learned about Peano's Axioms yet? If not, I think you will enjoy reading about them:donglepuss said:find me an integer that isn't divisible by 1.
An integer is a whole number, either positive or negative, including zero. It does not contain any fractions or decimals.
Yes, 1 is the only integer that can be derived from 1. This is because 1 is the smallest and only factor of itself.
No, negative integers cannot be derived from 1. This is because 1 can only be multiplied by itself to equal 1, and multiplying by a negative number would result in a negative product.
No, there are no exceptions to this statement. Every integer, positive or negative, can be derived from 1 through multiplication or addition.
The concept of "deriving from 1" is closely related to factorization. When we say that an integer is derived from 1, it means that 1 is a factor of that integer. In other words, the integer can be expressed as the product of 1 and another number, which is its factor. This is essentially the process of factorization.