MATH SOLVE

4 months ago

Q:
# There exists an m that belongs to the natural numbers such that for all n that belongs to the natural numbers it is true that 5 times m cubed is greater than or equal to divided by 3. Is it true or false?

Accepted Solution

A:

The statement is **false**. Let's see why:
Let's assume that the statement is true and there exists such an `m`. Then, for any `n` that belongs to the natural numbers, we have: 5m^3 > n/3
Multiplying both sides by `3`, we get: 15m^3 > n
Now, let's take `n = 15m^3 + 1`. Substituting this value of `n` in the above inequality, we get:
15m^3 > 15m^3 + 1
This is a contradiction because the left side is equal to `15m^3` while the right side is greater than `15m^3`. Hence, our assumption that the statement is true must be false. Therefore, the statement is **false**.