What is the property x*anything = x called? For instance infinity * 2 = infinity

Question

aravindg · Answer

Are you referring to the identity property?

mertsj · Answer

Multiplicative Identity Property

kainui · Answer

Nearly everything is the multiplicative identity of infinity haha, alright I guess that works. I just thought it was a bit different and had some other name, thanks.

samigupta8 · Answer

Hold on! Multiplicative identity is the property when we get the same number when it's multiplied with 1 and not any other number..Isn't it??
And here in your question, you remarked that x multiplied with anything gives x .So how is it going to be that identity?

kainui · Answer

I see what you're asking. Here, I'll show what I mean:

$$a*b =a$$

this is true when $b=1$ for all $a$. which is what you're thinking.

But this is also true if $a=\infty$ and for all $b > 0$ too.

samigupta8 · Answer

Correct ! But not for any other value of 'a' than infinity

samigupta8 · Answer

Ain't it?

kainui · Answer

$-\infty$ I guess haha but past that I don't know. Depends on how serious you want to get with this, if a and b were matrices we could easily end up with some other alternatives.

samigupta8 · Answer

Ah! I see .Here, i were restricting myself to the numbers though!

bobo-i-bo · Answer

Hmmm, look up the "zero product property". Might be something like that.

samigupta8 · Answer

Well! Still kai do you think that this property is multipliactive identity?

samigupta8 · Answer

I completely agree with your notion that infinity multiplied with a number gives infinity but this is not what multiplicative identity refers to .

samigupta8 · Answer

@bobo-i-bo what about that instance kainui adressed to ? I mean when infinity is multiplied with any number what will you call that property then?

kainui · Answer

Yeah I don't quite think that it's really what multiplicative identity refers to either. Beats me though, it's not too important I just wanted to know what to call this since I wanted to explain this idea to someone for a derivation with convolutions.

samigupta8 · Answer

Sounds good then! Whatever it is you might have been quite successful in explaining the better understanding of this property though!

bobo-i-bo · Answer

Here: https://proofwiki.org/wiki/Definition:Extended_Real_Multiplication https://proofwiki.org/wiki/Definition:Extended_Real_Addition https://proofwiki.org/wiki/Definition:Extended_Real_Number_Line

bobo-i-bo · Answer

Hmmm, not sure it completely captures the idea in question... I wish to say something more along the lines of "singular multiplication/addition". '~'