【Infinite】 , 【eternal】 ,  【sempiternal】 ,  【boundless】 ,  【illimitable】 ,  【uncircumscribed】  mean having neither beginning nor end or being without known limits.

【Infinite】 especially as applied to God or his attributes implies immeasurability or an incapacity for being estimated in any conceivable respect (as duration or extent).

In mathematical and scientific use the term usually stresses indeterminableness; often it implies that no limits can be set to which a thing does or may extend, or that no point at which it ends can be discerned; thus, the number of positive integers is  【infinite】  since no one can set a limit to the number that can be indicated; an  【infinite】 decimal is one (as a repeating decimal) that cannot be brought to a termination.

In more general use,  【infinite】 usually implies not only exceeding greatness or vastness but indefiniteness or seeming endlessness of extent.

【Eternal】 , in its earliest and still prevailing sense, implies having neither beginning nor end in time; it is therefore applied chiefly to God, in the sense of being uncaused or uncreated and unending. But it may be applied with essentially the same meaning to things and especially to abstractions and concepts for which no beginning is known or under present conditions is discoverable, and for which no end can be foreseen or predicted.

In more general use  【eternal】  may be indistinguishable in meaning from endless and is then applied to things with a known or evident beginning but no ending or an ending infinitely remote or completely indeterminable. This sense is frequent in hyperbolic use in which it may imply either endless duration or constant recurrence often to the point of weariness or disgust, but it also applies to something which, though it changes in appearance, form, or method, never dies out.

【Sempiternal】 , a bookish word, is an intensive of  【eternal】 with somewhat greater emphasis upon the continuity of the thing so described, but it is chiefly a hyperbolic term.

【Boundless】 implies little more than an apparent lack of restrictions or bounds, or a capacity for extending, expanding, or increasing indefinitely; it often applies to something which so far exceeds in range, measure, or amount what is usual for a thing of its kind that it staggers the mind. In mathematical and scientific usage,  【boundless】 applies specifically to a surface or a space (as a closed curved line or a spherical surface) which has the property of permitting an object starting from any point in the space and proceeding by one mathematical law to return to the same point without being interrupted.

【Illimitable】  also stresses a lack of bounds or limits, and may be used in place of  【boundless】 , but it is often applied specifically to something (as a distance) that can theoretically be measured in extent but in actuality exceeds the capacity of human ingenuity or of human instruments for measurement or determination of extent.

【Uncircumscribed】 implies the lack of a determinable limit in any conceivable direction; it applies to something that extends or expands or seems to extend or expand in all directions in the manner of radii from the center of a circle.