Does Everything Have to Always Make Sense?

The size of the set of all positive numbers is infinite.
The size of the set of all positive and negative numbers is infinite.
The entirety of the first set is contained within the second set.
Which set is bigger?
Is infinite not infinite?
Can one example of infinity be greater than another?
Does everything have to always make sense?
Let me make no sense (I am good at that)
the finite (positive or negative/rational or irrational numbers) cannot approach the infinite,
they are from two different realms.
Which is bigger?
Since one cannot approach the other...neither.
I told you I'd make no sense.
 
Let me make no sense (I am good at that)
the finite (positive or negative/rational or irrational numbers) cannot approach the infinite,
they are from two different realms.
Which is bigger?
Since one cannot approach the other...neither.
I told you I'd make no sense.
It's not about which number is bigger, but rather which set is larger.

Consider the following sets:

The set of all positive integers
[1, 2, 3, 4, ... infinity]

The set of all positive and negative integers
[negative infinity, ... -4, -3, -2, -1, 0, 1, 2, 3, 4, ... infinity]

Both sets are the same size in that both are infinitely large. However, the second set contains the entirety of the first set so the second set is larger.
 
It's not about which number is bigger, but rather which set is larger.

Consider the following sets:

The set of all positive integers
[1, 2, 3, 4, ... infinity]

The set of all positive and negative integers
[negative infinity, ... -4, -3, -2, -1, 0, 1, 2, 3, 4, ... infinity]

Both sets are the same size in that both are infinitely large. However, the second set contains the entirety of the first set so the second set is larger.
Here is how I understood it. Your first sentence was, "The size of the set of all positive numbers is infinite." Your second sentence was similar.
My point is that it's impossible for any set/positive numbers to be infinite or even reach infinite size, because if you think about it... take the largest set of numbers (or number) you can conceive of..then, just add 'one'. This is why natural numbers cannot be infinite or even reach/approach infinity.
This is more or less a picture of the impossibility of man (the finite) trying to reach God (the Infinite).
It took instead, God becoming finite to reach man.
I know, I know in mathematics they have a term 'approaching infinity's, but as a bible believer with some mathematical background, I'd say that is misleading.
You may have had a completely different point, if so, I'm sorry I misunderstood.
 
My point is that it's impossible for any set/positive numbers to be infinite or even reach infinite size, because if you think about it... take the largest set of numbers (or number) you can conceive of..then, just add 'one'.
I wasn't thinking of the mechanics of approaching infinity since that's a kind of Zeno's Paradox, but thanks for mentioning this. Rather, I was thinking of `infinity` as a done-deal, i.e. a logical concept.

This is more or less a picture of the impossibility of man (the finite) trying to reach God (the Infinite).
It took instead, God becoming finite to reach man.
I love how you tied these two concepts together! ❤️ Bravo! 👏
 
The size of the set of all positive numbers is infinite.
The size of the set of all positive and negative numbers is infinite.
The entirety of the first set is contained within the second set.
Which set is bigger?
Is infinite not infinite?
Can one example of infinity be greater than another?
Does everything have to always make sense?
Joe Biden is in America's White House, so I'd say the answer to the OP question is, no.
 
The size of the set of all positive numbers is infinite. The size of the set of all positive and negative numbers is infinite. The entirety of the first set is contained within the second set. Which set is bigger? Is infinite not infinite? Can one example of infinity be greater than another? Does everything have to always make sense?

Hello LearningToLetGo, I'll put a bit of a different twist on this (because this is what often seems to come from a mind as different as mine is ;)). My answer to your question is "no", because we know there are many things that are/will remain mysterious to us (to one degree or another) on this side of the grave, but it is also wonderful to remember/consider that everything that we ~need~ to understand, everything that ~needs~ to make sense to us, will (because God has made it so by revealing all of those things to us, and by giving us, His saints, the ability that we need to know, accept, and understand all of the necessary things from His spiritual POV .. e.g. 1 Corinthians 2:12-16 cf John 3:3, AMEN :)).
God bless you!! --Papa Smurf
p.s. - I apologize for the thread drift, and I hope that this doesn't cause any problems for your thread (it's just where my mind went when I read the last sentence in your OP).


Deuteronomy 29
29 The secret things belong to the LORD our God, but the things revealed belong to us and to our sons forever, that we may observe all the words of this law.

Hello LearningToLetGo;

During our vacation last week I checked in with CFS. I'm on other side of the world when I read brother LearningToLetGo's thread, Does Everything Always Have To Make Sense?

I have to admit I was scratching my head over the formula and in my limited thinking, this sounds respectfully like a software engineer. Before I retired from my work I was employed at a former company called A9.com, a search engine in Palo Alto, CA. I worked in the accounting field and confess many times I didn't know shiite from shinola when the engineers discussed work. Many times they had white boards in their offices with these math formulas and terminology. I would overhear the engineers discuss things that I did not understand.

But when they submitted their expense reports to me it was my turn to explain and help them understand how their expenses would allocate to the various chart of accounts. Ironically, I was never a good math student and never got past algebra but studied debits, credits and business math during my accounting college years.

I began to go out to lunch with some of the guys and when they explained some of my elementary questions about their work, at some point they talked of a "higher power" in the discussion and how the
advanced speed of science technology, the internet and algorithms, they would quote, "made no sense!" Therefore, the desire to study or the requirement to study in this field was needed to keep up and no doubt goes on today.

Papa Smurf, thank you, brother, for bringing this topic back to the center of Christ which caused this thought to fill my limited knowledge.

Does everything in life or my life, always have to make sense?
No. Only everything with God makes sense;

Isaiah 55:8-9, 8 For my thoughts are not your thoughts, neither are your ways my ways, declares the Lord. 9 For as the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts.

God will reveal only what we need to know since we cannot master His ways. God is God, and we are human. "The difference and distance between God and man is revealed, not to discourage us from seeking Him, but to keep us humble as we seek. “You may conclude that it is not intended that you should understand the infinite, for you are told that his thoughts and ways are far above you;" - quote Spurgeon

Thank you for sharing this topic, LearningToLetGo.

God bless you, brother, and your family.
 
I have to admit I was scratching my head over the formula and in my limited thinking, this sounds respectfully like a software engineer. Before I retired from my work I was employed at a former company called A9.com, a search engine in Palo Alto, CA. I worked in the accounting field and confess many times I didn't know shiite from shinola when the engineers discussed work. Many times they had white boards in their offices with these math formulas and terminology. I would overhear the engineers discuss things that I did not understand.

But when they submitted their expense reports to me it was my turn to explain and help them understand how their expenses would allocate to the various chart of accounts. Ironically, I was never a good math student and never got past algebra but studied debits, credits and business math during my accounting college years.
Story of my life. I'm a computer programmer who writes accounting software. In fact, it's the end of month so we're knee deep in the muck as I type. :)
 
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