I think there is no difference. Ask your friend why he thinks that these are not same in mathematical standpoint.

I am not mathematician, but I "suppose" the difference between the two is the degree of certainty. An assumption entails a greater degree of certainty than a supposition. Let's see what the colleagues have to offer.

For me, "assume" involves a small difference, for example, if we carry out the algebraic expansion of (1 + cosA)**10, then when A is close to 90 degrees or pi/2 radians, we can ASSUME that this function is equivalent to 1 + 10cosA (as the other terms are so small that they can be disregarded).
Suppose, on the other hand, involves a greater shift in line of thought.

Hope this helps to elucidate this subtle difference.

English term (edited): assumption vs. supposition

if you look at fundamental mathematical sites (like university math departments, see MIT link below) showing proofs, you will see this.

Since the answer is unknown, neither nor is in the mind of the mathematician. Therefore, according to the constructivists, the disjunction is not a legitimate mathematical assumption. Thus Aristotle's either-or principle (see 1.1.1 and 1.2.3 above) must be abandoned.

CILT - Mathematics Standards Glossary
... Mathematics - Glossary. Absolute Value, ... x. Axiom, A basic assumption about a mathematical system from which theorems can be deduced. For ...
164.64.166.11/cilt/standards/math/glossary.html

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Note added at 9 hrs 34 mins (2004-07-11 22:03:14 GMT)
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Math is black or white except in hypothetical cases, when substituting different values for a variable.

In the asker\'s example we are dealing with a hypothetical, so both terms can be used. I added my entry because I thought it might be helpful to the asker in general.

In Pike\'s example below :
Given formula a = G*c
if variable c = 1, then.....
if varable c = 2, then

this type of hypothetical phrasing (given x = 1 + y) If y = 1, then x = blahblah
If y = 2, then

the same type of hypothetical phrase is used in regular everyday English: if I use 2 eggs instead of 1, I will need 3 cups of flour.

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Note added at 9 hrs 38 mins (2004-07-11 22:06:52 GMT)
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this type of hypothetical reasoning is really an exercise in deductive logic

Assume: The trial declaration, effort made by the reader; A and B are forced to be equal by the subject. A and B have nothing to do themselves. They are helpless.


Suppose : The subject/ author has less role. A & B together/ willingly agree to be equal. And it is a chance; trial made by the author/subject. A and B cooperate for the exercise.