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'DPI' stands for dots per inch. It is a crucial unit of measure applied in print media, and recently in digital media as well, to define the resolution of an image or a printed text. By definition, a DPI denotes how many dots a printer can fit into a one-inch space. For instance, an image with a 300 DPI resolution will possess 300 dots within a one-inch space. DPI, thus, serves as an integral determinant of the clarity, sharpness, and detail levels in images.

The concept of DPI finds its roots in the print industry. For decades, the print service providers have been using DPI as a metric for expressing the resolution of the images produced by their printing machines. It has always been a standard practice among these providers to specify the DPI values of their printers, as a higher DPI value typically translates into better image quality with more detail, clarity, and sharpness. When the number of dots is high, there is more detail in the image, which gives it a crisp look. However, it is also important to note that a higher DPI value leads to more ink consumption, which can increase the cost of printing.

In the digital sphere, DPI plays a similar role. When you're working on a digital image, the DPI value determines how sharp the image will be when it's eventually printed. More specifically, a higher DPI value leads to a more detailed and sharp image on screen. Similar to the print industry, a higher DPI value in the digital space also means that the file size of the image will be larger because there's more pixel information to store.

However, the notion of DPI in the digital world has been the subject of much debate. Some argue that DPI is irrelevant when it comes to digital displays because they have a fixed resolution that cannot be changed by increasing or decreasing the DPI of an image. This view holds that the DPI value in digital images only becomes pertinent when the image is printed. This argument notwithstanding, DPI continues to be used as a standard metric for measuring image resolution in the digital space.

In conclusion, DPI is a crucial metric that determines the quality of both printed and digital images. It influences the clarity, detail, and sharpness of an image as well as the file size when it comes to digital imagery. Despite some criticisms about its relevance in the digital realm, it remains a widely used term in both digital and print industries.