Claim: If R is a ring with unity, it is unique. If α∈R is a unity, then its multiplicative inverse is unique.
My proof Let R be a ring with unity. Suppose β1,β2∈R both satisfy the properties of being a unity. Then ∀α∈R we have
Hence from (1) and (2)we have
This means that either α=0 or β1−β2=0
If α=0 (here is my struggle case, anything multiplied by 0 is 0 so I dont know what to say, or how this case implies that β1=β)
If α≠0 then β1−β2=0β which means β1=β2. Hence unity is unique.
The other part im okay with. Thank you
reaches the maximum height of 50 m. another body with double the mass thrown
sorry question i can't
yrr ok say
what u want bit**