Math Is Fun Forum

It only happens when r = 3. This is because

so

. Hence the surface area and the volume of a sphere are numerically equal if and only if its radius is 3.

PS: It has nothing to do with the value of pi.

Every integer can be expressed as the sum of two or more consecutive integers.

And so on.

The statements are not the same. In statement 1, one single d holds for all a; in statement 2, different a may be associated with different d. Statement 2 only says that there exists at least one d for each a.

This distinction is the difference between continuity and uniform continuity. Let I be a real interval and ƒ a real-valued function on I. Then:

(i)  ƒ is continuous on I iff
(∀ε>0)(∀x∈I)(∃δ>0)(∀y∈I)(|x−y|<δ⇒|ƒ(x)−ƒ(y)|<ε)

(ii) ƒ is uniformly continuous on I iff
(∀ε>0)(∃δ>0)(∀x∈I)(∀y∈I)(|x−y|<δ⇒|ƒ(x)−ƒ(y)|<ε)

The two definitions are different. In (i) δ depends on x; different δ may need to be chosen for different x. In (ii), one single δ has to work for all x.

Hi luckyleafs! Welcome to the forum.

rhymin posts on at least two other math forums (besides this one). From the questions I’ve seen him/her ask, I would say he/she is a mature learner trying teaching himself/herself maths.

It certainly is. Lima also means 5 in Malay and Indonesian.

Next: 6 in Tagalog is anim.

I think the numbering of the questions should be more consistent.

So, we generalize the problem as follows:

Find the smallest natural number of two or more digits such that if you move the last digit to the front, the resulting number will be n times the original number.

Here are my calculations:

March 14 is also the birthday of Albert Einstein. A very auspicious day for the math & science community indeed.