# Does an inverse Riemann exist?

• I
• smilodont

#### smilodont

I already googled this but I did not find a definite answer. Is there such a thing as a 'inverse riemann'? Specifically, where you invert the start number to be at the top of the riemann symbol and then decrement down to the end value which is on the bottom of the riemann symbol?

Thereis nothing special about the integral you described. Switching the end points simply means changing the sign of the integral.

Ok, explain what you mean. I had never seen that before.

Do you mean ##g(x):= \int_a^x f(t)dt ## , where x is a variable?

Ok, explain what you mean. I had never seen that before.
$\int_a^bf(x)dx=-\int_b^af(x)dx$

Smilodont: The name "Riemann" is associated with so many concepts that it would help a lot if you spelled out what you mean in some detail.

∑ is a riemann. You pointed out an integral. They are similar but not the same. I am talking about the riemann sum. hope that clarifies.

Riemann sum is used as approximation to Riemann integral. In that context what exactly is your question?

i am interested in the ∑ use. i was confused in calling it a riemann sum. too long since college. it's a summation symbol. what i was interested in is if you can put the higher value on the bottom and lower value on the top. If so, is that viewed as indicating you wish to decrement from the value at the top to the value at the bottom?

∑ is a riemann.
No, the symbol ∑ represents a sum or summation. As far as I know there is no such thing as "a riemann," short of being a reference to someone with that name.
smilodont said:
You pointed out an integral. They are similar but not the same. I am talking about the riemann sum. hope that clarifies.

A summation typically looks something like this:
$$\sum_{j = 1}^n a_j$$
The index starts at the value at the bottom and increases up through the upper value above the summation symbol. I've never seen a summation where the index was decremented, and I don't think there is any commonly used notation to indicate this.