Convention regarding inclusion of both an abstract and introduction in a mathematical paper Good afternoon,

I am a high school junior in the process of preparing a real analysis paper for submission to a mathematics journal. I have written my proof and conducted an exhaustive literature review and now I would like to take the next step towards finishing my paper but I am unclear as to the convention with regards to including in my paper both an abstract and introduction or just an introduction.  

I have read published papers such as this one by Erdos which include both an abstract and introduction but I have read many others such as this short proof of the prime number theorem which includes just an introduction. Then there are some like this one that have what appears to be an abstract without an explicit heading.

I have also read guides regarding how to write mathematical papers. There is this one which includes an introduction but no abstract. Then there are other guides like this one which make mention of both an abstract and an introduction.

My question is, is there a convention regarding the inclusion of an abstract in a math paper? If so, what is it? I understand that scientific papers traditionally employ both but I do not see a trend when it comes to math papers. 

Thank you in advance.
The purpose of an abstract and an introduction are very different, so it may be useful to include either or both. An abstract is a summary of the whole paper, focusing on the main result. It might exist separately from the paper itself as, say, an online "teaser" to get people to read the paper. But an introduction is intended to give background on the problem to be addressed in the paper and to situate it within the literature. You would almost always include an introduction. You might also write the abstract, but not actually include it within the paper itself.