Sin or sins?

Hi. Could we use the word "sin" to mean generally and also to encompass (I hope this is the right word for this context - not sure, though) the innumerable sins that have been committed possibly over thousands of years?

Glory to the Lamb of God who took away the sin of the world.

Also could we use the word "transgression" to refer to a multitude of sins committed for a long period of time? Sorry for not giving you (providing you with) a complete example sentence. Thank you for your help in advance.

Their transgression has given a way to ...