Participant with $0 Compensation and 401(k) testing

[Guest f1234]

We have a client (C-Corp) with two owners that sponsors a non Safe Harbor 401(k) Plan. This year, one of the owners did not receive any compensation. For ADP testing, is he treated as a 0% deferral or does he need to be omitted from the testing?

Thank you for your assistance.

[WDIK]

One of numerous lively debates can be found here.

[Belgarath]

After reading the debate, I throw this out to add fuel to the fire. Let me first add that I have no choice but to take the word of my betters when it comes to mathematics, as I can't count my toes twice and get the same number. Fortunately, our daughter is a math whiz, so she can usually explain things to her mathematically challenged parents. (I'm fine with numbers, it's just abstract concepts where the rot sets in...)

Why can't you divide by 0?

Why is 0/0 "indeterminate" and 1/0 "undefined"?

Why is dividing by zero "illegal"?

Here, in their own words, are some explanations by our 'math doctors'. Follow the links to read the full answers in the Dr. Math archives.

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Division by zero

Division by zero is an operation for which you cannot find an answer, so it is disallowed. You can understand why if you think about how division and multiplication are related.

12 divided by 6 is 2 because

6 times 2 is 12

12 divided by 0 is x would mean that

0 times x = 12

But no value would work for x because 0 times any number is 0. So division by zero doesn't work.

- Doctor Robert

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My teacher says you can't divide a number by zero. Why?

Let's look at some examples of dividing other numbers.

10/2 = 5 This means that if you had ten blocks, you could

separate them into five groups of two.

9/3 = 3 This means that if you had nine blocks, you could

separate them into three groups of three.

5/1 = 5 Five blocks could be separated into five groups

of one.

5/0 = ? Into how many groups of zero could you separate

five blocks?

It doesn't matter how many groups of zero you have, because they would never add up to five since 0+0+0+0+0+0 = 0. You could even have one million groups of zero blocks, and they would still add up to zero. So, it doesn't make sense to divide by zero since there is not a good answer.

If you know a little bit about multiplication, you could look at it this way:

10/2 = 5 This means that 5 x 2 = 10

9/3 = 3 This means that 3 x 3 = 9

5/1 = 5 This means that 5 x 1 = 5

5/0 = ? This would mean that the answer x 0 = 5, but

anything times 0 is always zero.

So there isn't an answer.

- Dr. Margaret

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Why can't you divide a number by 0?

For one thing, when you divide one number by another, you expect the result to be another number. Look at the sequence of numbers 1/(1/2), 1/(1/3), 1/(1/4), ... . Notice that the bottoms of the fractions are 1/2, 1/3, 1/4, ..., and that they're going to zero. If there's a limit to this sequence, we would take that number and call it 1/0, so let's see if there is.

Well, the sequence turns out to be 2, 3, 4, ..., and that goes to infinity. Since infinity isn't a real number, we don't assign any value to 1/0. We just say it's undefined.

But let's say we did assign a value. Let's say that infinity is a real number, and 1/0 is infinity. Then look at the sequence 1/(-1/2), 1/(-1/3), 1/(-1/4), ..., and notice again that the denominators -1/2, -1/3, -1/4, ..., are going to zero. So again, we would want the limit of this sequence to be 1/0. But looking at the sequence, it simplifies to -2, -3, -4, ..., and it goes to negative infinity. So which would we assign to 1/0? Negative infinity or positive infinity? Instead of just assigning one willy nilly, we say that infinity isn't a number, and that 1/0 is undefined.

- Dr. Ken

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When something is divided by 0, why is the answer undefined?

The reason is related to the associated multiplication question. If you divide 6 by 3 the answer is 2 because 2 times 3 IS 6. If you divide 6 by zero, then you are asking the question, "What number times zero gives 6?" The answer to that one, of course, is no number, for we know that zero times any real number is zero not 6. So we say that division by zero is undefined, for it is not consistent with division by other numbers.

- Dr. Robert

Because there's just no sensible way to define it.

For example, we could say that 1/0 = 5. But there's a rule in arithmetic that a(b/a) = b, and if 1/0 = 5, 0(1/0) = 0*5 = 0 doesn't work, so you could never use the rule. If you changed every rule to specifically say that it doesn't work for zero in the denominator, what's the point of making 1/0 = 5 in the first place? You can't use any rules on it.

But maybe you're thinking of saying that 1/0 = infinity. Well then, what's "infinity"? How does it work in all the other equations?

Does infinity - infinity = 0?

Does 1 + infinity = infinity?

If so, the associative rule doesn't work, since (a+b)+c = a+(b+c) will not always work:

1 + (infinity - infinity) = 1 + 0 = 1, but

(1 + infinity) - infinity = infinity - infinity = 0.

You can try to make up a good set of rules, but it always leads to nonsense, so to avoid all the trouble we just say that it doesn't make sense to divide by zero.

What happens if you add apples to oranges? It just doesn't make sense, so the easiest thing is just to say that it doesn't make sense, or, as a mathematician would say, "it is undefined."

Maybe that's the best way to look at it. When, in mathematics, you see a statement like "operation XYZ is undefined", you should translate it in your head to "operation XYZ doesn't make sense."

- Dr. Tom

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What is the value of 0/0? (Is it really undefined or are there an infinite number of values?)

There's a special word for stuff like this, where you could conceivably give it any number of values. That word is "indeterminate." It's not the same as undefined. It essentially means that if it pops up somewhere, you don't know what its value will be in your case. For instance, if you have the limit as x->0 of x/x and of 7x/x, the expression will have a value of 1 in the first case and 7 in the second case. Indeterminate.

- Dr. Robert

[Tom Poje]

algebra 101

solve the following:

3(a - 2) = 5a - 10

simplify

3(a - 2) = 5 (a - 2)

divide both sides by (a - 2)

hence

3 = 5

[stephen]

Tom,

Shame on you-

3(a - 2) = 5a - 10

3a - 6 = 5a - 10

subtract 3a from both sides

-6 = 2a - 10

add 10 to both sides

4 = 2a

divide both sides by 2

2 = a

Check your work:

3(2 - 2) = 5*2-10; 3*0 = 10-10; 0=0

Your way does not work since you are dividing by zero... thus 3 does NOT equal 5.

Perhaps you can incorporate this into your song this year.

[E as in ERISA]

I think that was Tom's point? You can't divide by an unknown?

[Tom Poje]

correct Mr. ERISA.

Stephen - I have already decided to 'adapt' one of Louis Armstrong's songs.