True or False: Every number has a limited amount of factors, but an unlimited amount of multiples.

Mathematics

2 answers:

nalin [4]3 years ago

4 0

Answer:

False

Step-by-step explanation:

0 has unlimited numbers of factors because 0 times everything equals 0. If 0 is not included then the statement is true.

Irina18 [472]3 years ago

3 0

Answer:

true

Step-by-step explanation:

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Given that f(a+b)= f(a) + f(b) and f(x) is always positive, what os the value of f(0)?

FrozenT [24]

This is a strange question, and f(x) may not even exist. Why do I say that? Well..

[1] We know that f(a+b) = f(a) + f(b). Therefore, f(0+0) = f(0) + f(0). In other words, f(0) = f(0) + f(0). Subtracting, we see, f(0) - f(0) = f(0) or 0 = f(0).

[2] So, what's the problem? We found the answer, f(0) = 0, right? Maybe, but the second rule says that f(x) is always positive. However, f(0) = 0 is not positive!

Since there is a contradiction, we must either conclude that the single value f(0) does not exist, or that the entire function f(x) does not exist.

To fix this, we could instead say that "f(x) is always nonnegative" and then we would be safe.

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