Is assuming an infinity has somehow completed a contradiction to the concept of infinity?
No, because an infinity by definition must exist if a continuum is unbounded at EITHER end; AND may exist even where a continuum is bounded at BOTH ends.
An infinity does not exist.
Then you should have no problem in demonstrating that an infinite past necessarily entails a contradiction.
We're all waiting...
It is not assumed to exist.
Then you are going to have a very hard time demonstrating that an infinite past necessarily entails a contradiction. Thinking about stuff involves assuming things, to see where they lead you. If you refuse to think about something, then you will never know anything about it.
An infinity is defined. It is not discovered or observed in any way.
As long as you have a definition, you can make assumptions and test them for contradictions.
We're still waiting...
And as it is defined, as it is imagined, it does not have the ability to ever be completed. The elements within an infinite series could never all be expressed.
Non sequitur fallacy. Unless you can demonstrate that they must be 'expressed' (you will need to start by defining 'expressed'), this is not helping you to demonstrate a contradiction inherent in assuming that an infinite past existed.
If you had to actually express every fraction between zero and one it could not be done.
And yet, we know that there are an infinite number of such fractions. You appear to be arguing against your stated position here.
But you can draw a line, pretend it is imaginary, and then pretend all the fractions exist within the finite space.
You could do all sorts of strange things. But you have not shown that this is in any way relevant to the demonstration that an infinite past necessarily entails a contradiction, which is your task (and your ONLY task), if you are to demonstrate the truth of your claim that an infinite past is impossible.
You appear to be getting bogged down in analogies that you cannot (or will not; certainly you HAVE not) shown to be in any way relevant to the question at hand.
Please, stick to the question - or, if you need to invoke drawn lines, imaginary lines, fractions between 0 and 1, and all these other things, show in detail how they are relevant to the question at hand. You are claiming that the existence of an infinite past is impossible. You can ONLY support that claim by demonstrating that it entails a contradiction. If you can do that, then please stop wasting our time, and do it. If you cannot do that, have the wit and the grace to admit that your certainty is misplaced, and that you do not KNOW it to be impossible - that you just think it's unlikely.
You have not demonstrated that there is no contradiction between the definition of an infinity and a completed infinity.
Shifting the burden of proof didn't work before; What makes you imagine that it is suddenly not a fallacy now?
So since a clear contradiction exists we are done.
No clear contradiction has been presented. You just declared that I needed to demonstrate that one does not, which is the (rather tired) logical fallacy of shifting the burden of proof.
I think you need to learn how to think; You are clearly unqualified to attempt the proof that you are trying to achieve.