Needing a basic clarification with SR

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I am new to understanding the concepts in SR and GR, and one of the main concepts i am having difficulty with is the speed limit. I don't understand why things can't already be moving at the speed of light in certain frames of reference. For instance, from the Earth's frame of reference, isn't it possible for something to be traveling c/2 in one direction and something else to be traveling at c/2 in the exact opposite direction, making the velocity from either object's frame of reference c?
 
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No, look up velocity addition in wikipedia.
 
Thanks!
 
These equations on velocity addition are based off time dilation, correct?
 
jam.muskopf said:
These equations on velocity addition are based off time dilation, correct?

No, they are based on the postulate (or empirical observation) that all observers measure the speed of light to be c, regardless of their frame of reference.
 

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