What is the argument this is a proof and not an assumption? ... what logical step have you taken here? ... and go ahead and apply this logic to the CMB Epoch as a demonstration ...
Total gibberish with a smidgen of word-salad dressing, the CMB epoch, poured on top.
(By the way, that's the second time I posted the excerpt from my article in this thread. You should have read it the first time.)
The summation of the Kalam Cosmological Argument below the accompanying videos of the same in the OP stand and stay.
The ball is in your court. It's for you to disprove the argument, and the only way you can do that is to show how an infinite chain of causal events regressing into the past forever could ever possibly be traversed to the present. Either you can coherently show that or you can't, and, of course, you can't. No one can. Actual infinities only exist in minds as mathematical concepts. They have absolutely no existentiality outside of minds, and the notion of an infinite regress of causal events being traversed to the present is an absurdity. Period!
And just as you incessantly misstated my observations due to your obvious ignorance regarding the distinction between potential and actual infinities, and the ramifications thereof
—I seriously doubt you understand what the essence of the Epsilon-Delta Proof (ε - δ definition of a limit) is, given that the most straightforward mathematical illustration of the existential impossibility of an actually infinite regress in nature would entail a limit function of systematic division.
Excerpt from my article:
But, once again, what do we do with any given integer divided by Infinity? The quotient would obviously not equal ±∞. Nor would it equal 0. If we were to divide ±1 by ∞, for example, and say that the quotient were 0, then what happened to ±1? Calculus entails the analysis of algebraic expressions in terms of limits, so in calculus the expression n ÷ ∞ = 0 doesn't mean the quotient literally equals 0. Rather, 0 is the value to which the quotient converges (or approaches). Again, Infinity is a concept, not a number. We can approach Infinity if we count higher and higher, but we can't ever actually reach it. Though not an indeterminate form proper, n ÷ ∞, like any other calculation with Infinity, is technically undefined. Notwithstanding, we intuitively understand that ±1 ÷ ∞ equals an infinitesimally small positive or negative number. Hence, we could intuitively say that ±1 ÷ ∞ = ±0.000 . . . 1, and we would be correct.
For the proof, let the input variable = x, and let the integer = 1:
x | 1 ÷ x |
1 | 1 |
2 | 0.5 |
4 | 0.25 |
10 | 0.1 |
100 | 0.01 |
1,000 | 0.001 |
10,000 | 0.0001 |
100,000 | 0.00001 |
1,000,000 . . . | 0.000001 . . . |
Note that as x gets larger and larger, approaching Infinity, 1 ÷ x gets smaller and smaller, approaching 0. The latter is the limit, and because we can't get a final value for 1 ÷ ∞, the limit of 1 ÷ x as x approaches Infinity is as good as we're going to get. The limit of a function in calculus tells us what value the function approaches as the x of the function (or, in shorthand, the x of the f ) approaches a certain value:
lim f(x)
x→a
We know that we're proving the limit for 1 ÷ ∞; hence, the following reads "the limit of the function f(x) is 1 ÷ x as x approaches Infinity":
f(x) = lim 1 ÷ x
x→∞
Additionally, the output values of function f depend on the input values for the variable x. In the expression f(x), f is the name of the function and (x) denotes that x is the variable of the function. The function itself is "the limit of 1 ÷ x as the inputs for x approach Infinity." When we solve for the limit of more than one function in an algebraic combination, we typically call the first of the functions f for "function." It really doesn't matter what we call any of them as long as we distinguish them from one another. The names given to the others typically follow f in alphabetical order merely as a matter of aesthetics: g, h, i, j and so on.
Hence, as we can see from the table above, the function proves out that the limit of 1 ÷ x as x approaches Infinity is 0. That is, as x approaches Infinity, 1 ÷ x approaches 0.
lim 1 ÷ x = 0
x→∞
Altogether then:
lim f(x) = lim 1 ÷ x = 0 (i.e., 0.000 . . . 1)
x→a x→∞
| x | 1 ÷ x |
| 1 | 1 |
| 2 | 0.5 |
| 4 | 0.25 |
| 10 | 0.1 |
| 100 | 0.01 |
| 1,000 | 0.001 |
| 10,000 | 0.0001 |
| 100,000 | 0.00001 |
| 1,000,000 . . . | 0.000001 . . . |
In nature
t = 0 is never reached via an infinite regress into the past. Hence, an infinite regression can never be traversed to the present.
Check and mate!
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