I'm no math guru

[born2laser]

(Yesterday 09:34 PM)Maximilian Hohmann Wrote:  Hello!

(Yesterday 08:47 PM)Josef Wrote:  Nowadays, just ask e.g. chatGPT and they will solve similar tasks instantly with justification.

Today it was in the news here in Germany, that students who use AI tools learn better and have a better learning experience than those who don't!

So let's go for it! For this, I asked "Claude" because lately the free version of ChatGPT is quite slow due to large demand.

Please solve X = X / 5 for x

Claude:
Let me solve this algebraic equation step by step:
X = X / 5
To solve for X, we'll multiply both sides by 5:
5X = X
Subtract X from both sides:
4X = 0
Divide both sides by 4:
X = 0
Therefore, the only solution to the equation X = X / 5 is X = 0.
Let's verify:

When X = 0:
0 = 0 / 5
0 = 0 ✓

This means that 0 is the only value that satisfies the equation X = X / 5.

Would infinity also solve this equation?

Let me carefully examine this claim.
If X = X / 5, we want to check if infinity (∞) works:
∞ = ∞ / 5
This reveals an interesting mathematical nuance. In standard real number arithmetic, this is undefined because:

Division of infinity by 5 would still be infinity
But the equation ∞ = ∞ / 5 suggests 5 × 1 = 1, which is mathematically inconsistent

In the extended real number system or in some interpretations of limits, this might behave differently. However, in standard algebraic manipulation, infinity is not a number that solves X = X / 5.
The rigorous solution remains X = 0, which is the only real number that satisfies the equation:

0 = 0 / 5
0 = 0 ✓

The key point is that for the equation to be true, the value of X must be zero, where dividing by 5 reduces the value to itself. Infinity does not meet this criterion.

An answer that even I (not in the least a math guru...) can understand!

Regards
Max

ugh!
The answer to the first question is correct, maybe because it had enough textbooks in the training set, but sort of misses the second one because it argues the question both ways.
The implicit assumption is that we are looking for solutions in the set of real numbers (or complex for that matter). If the chosen set is different the number of solutions is different, for example the equation has no solutions in the set of natural numbers, because that does not include the zero.
If you use the set that treats infinity as a number with all the weird properties that entails, you have to play by those rules and accept infinity as a solution.
I will take the position that -assuming the equation represents some real world problem- we are looking for solutions that may have real application, and thus I'll stick with the set of real numbers and zero is the only solution

Juan