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First, I wanted to personally reply to many answers and comments because of their relevance to this discussion but there are too many of them. So I just say thank you to everyone who answered or commented on ways to teach him this concept. This was important for me as I'm not a mathematician and in fact written a whole book in my branch of engineering using only the most basic operations. I will now accept @orion2112's answer as the most suitable for his age, and upvote the rest.

As noted above, he came up with his explanation a few minutes after I typed the question on this forum.

On a piece of paper (not instructed by me), he started with writing 10, then 100, then 1000, .... and he stopped after writing 40 zeros with 1. Then he came to me and said, "I understand infinity now; infinity is a number with infinite zeros."

The main point is that as most of you suggested, he has now registered infinity in his brain as a concept rather than a number, which is why he used the expression 'a number with infinite zeros'.

(Just in case it matters, I have taught him to read large numbers like this: e.g., for a 1 with 20 zeros, count to the nearest multiple of 9 and subtract it, that makes it 100 and then divide 18 by 9 to make it 2. So the number becomes 100 bilion billion. This is sometimes important because having the ability to count the numbers keeps the child's interest going).

On a piece of paper, he started with writing 10, then 100, then 1000, .... and he stopped after writing 40 zeros with 1. Then he came to me and said, "I understand infinity now; infinity is a number with infinite zeros."

The main point is that as most of you suggested, he has now registered infinity in his brain as a concept rather than a number, which is why he used the expression 'a number with infinite zeros'.

First, I wanted to personally reply to many answers and comments because of their relevance to this discussion but there are too many of them. So I just say thank you to everyone who answered or commented on ways to teach him this concept. This was important for me as I'm not a mathematician and in fact written a whole book in my branch of engineering using only the most basic operations. I will now accept @orion2112's answer as the most suitable for his age, and upvote the rest.

Having said that, he came up with his own answer a few minutes after I typed the question on this forum. So it seems better to write it as an answer here instead of a comment. Along with many other useful answers and comments above, this will be helpful to future questioners searching for the same to satisfy their children.

On a piece of paper (not instructed by me), he started with writing 10, then 100, then 1000, .... and he stopped after writing 40 zeros with 1. Then he came to me and said, "I understands infinity now; infinity is a number with infinite zeros."

The main point is that as most of you suggested, he has now registered infinity in his brain as a concept rather than a number, which is why he used the expression 'a number with infinite zeros'.

(Just in case it matters, I have taught him to read large numbers like this: e.g., for a 1 with 20 zeros, count to the nearest multiple of 9 and subtract it, that makes it 100 and then divide 18 by 9 to make it 2. So the number becomes 100 bilion billion. This is sometimes important because having the ability to count the numbers keeps the child's interest going).

First, I wanted to personally reply to many answers and comments because of their relevance to this discussion but there are too many of them. So I just say thank you to everyone who answered or commented on ways to teach him this concept. This was important for me as I'm not a mathematician and in fact written a whole book in my branch of engineering using only the most basic operations. I will now accept @orion2112's answer as the most suitable for his age, and upvote the rest.

As noted above, he came up with his explanation a few minutes after I typed the question on this forum.

On a piece of paper (not instructed by me), he started with writing 10, then 100, then 1000, .... and he stopped after writing 40 zeros with 1. Then he came to me and said, "I understand infinity now; infinity is a number with infinite zeros."

The main point is that as most of you suggested, he has now registered infinity in his brain as a concept rather than a number, which is why he used the expression 'a number with infinite zeros'.

(Just in case it matters, I have taught him to read large numbers like this: e.g., for a 1 with 20 zeros, count to the nearest multiple of 9 and subtract it, that makes it 100 and then divide 18 by 9 to make it 2. So the number becomes 100 bilion billion. This is sometimes important because having the ability to count the numbers keeps the child's interest going).

First, I wanted to personally reply to many answers and comments because of their relevance to this discussion but there are too many of them. So I just say thank you to everyone who answered or commented on ways to teach him this concept. This was important for me as I'm not a mathematician and in fact written a whole book in my branch of engineering using only the most basic operations. I will now accept @orion2112's answer as the most suitable for his age, and upvote the rest.

Having said that, he came up with his own answer a few minutes after I typed the question on this forum. So it seems better to write it as an answer here instead of a comment. Along with many other useful answers and comments above, this will be helpful to future questioners searching for the same to satisfy their children.

On a piece of paper (not instructed by me), he started with writing 10, then 100, then 1000, .... and he stopped after writing 40 zeros with 1. Then he came to me and told that he understands infinity now; infinity is a number with infinite zeros :)

The main point is that as most of you suggested, he has now registered infinity in his brain as a concept rather than a number, which is why he used the expression 'a number with infinite zeros'.

(Just in case it matters, I have taught him to read large numbers like this: e.g., for a 1 with 20 zeros, count to the nearest multiple of 9 and subtract it, that makes it 100 and then divide 18 by 9 to make it 2. So the number becomes 100 bilion billion. This is sometimes important because having the ability to count the numbers keeps the child's interest going).

First, I wanted to personally reply to many answers and comments because of their relevance to this discussion but there are too many of them. So I just say thank you to everyone who answered or commented on ways to teach him this concept. This was important for me as I'm not a mathematician and in fact written a whole book in my branch of engineering using only the most basic operations. I will now accept @orion2112's answer as the most suitable for his age, and upvote the rest.

Having said that, he came up with his own answer a few minutes after I typed the question on this forum. So it seems better to write it as an answer here instead of a comment. Along with many other useful answers and comments above, this will be helpful to future questioners searching for the same to satisfy their children.

On a piece of paper (not instructed by me), he started with writing 10, then 100, then 1000, .... and he stopped after writing 40 zeros with 1. Then he came to me and said, "I understands infinity now; infinity is a number with infinite zeros."

The main point is that as most of you suggested, he has now registered infinity in his brain as a concept rather than a number, which is why he used the expression 'a number with infinite zeros'.

(Just in case it matters, I have taught him to read large numbers like this: e.g., for a 1 with 20 zeros, count to the nearest multiple of 9 and subtract it, that makes it 100 and then divide 18 by 9 to make it 2. So the number becomes 100 bilion billion. This is sometimes important because having the ability to count the numbers keeps the child's interest going).